The national picture is looking extremely bleak, with the exception of Maryland, which is looking merely very bleak. (I have no clue what’s going on in Idaho. Either they aren’t reporting data or Covid Act Now can’t interpret it.)

The most dangerous areas used to be colored bright red, meaning “Very High Risk,” until things got so bad during the third surge of 2020 that the whole map was bright red and they decided to add a new dark red “Extremely High Risk” to differentiate between regions that were bad and regions that were extremely bad.

At the high end of the scale, risk is driven almost entirely by the daily new case rate. So thanks to Omicron’s high infectivity, almost everything is the same color again. Basically, it’s all bad. Covid is everywhere. And looking at the historic daily new case data, it’s clear things are pretty bad:

As you can see, this recent surge in Covid cases is much higher than any previous surge of cases, including last year’s brutal winter brutal wave. (The first wave is likely understated due to lack of testing, but I doubt it was this bad.)

The good news is that a lot of people are vaccinated, and that Omicron seems to be a bit less dangerous than previous strains, which means that those cases don’t translate into hospitalizations and deaths the way earlier waves did.

In fact, some Covid skeptics have been dismissing this wave as a “casedemic,” meaning there are lots of cases, but little real harm. This is emphatically not true. Hospitalizations, for example, haven’t gone up in proportion to cases, indicating that this wave is less likely to require Covid patients to be hospitalized, but the number of cases is so much higher than before that the smaller proportion sent to the hospital still rose higher than even last winter’s wave:

(For an idea of what this is like for hospital workers, check out Andy Slavitt’s “A Day Inside the ER During Omicron” podcast, in which Dr. Megan Ranney explains what’s going on in her hospital’s emergency department during the Omicron wave.)

Fortunately, deaths have not followed the same pattern. Not that 2500 deaths/day is a good number, but it’s better than 3000.

Switching to Covid statistics here in the Chicago metro area, things are worse in some ways, better in others:

That recent data is confusing, so let’s zoom in on the last 60 days:

As you can see, despite a few reporting glitches, we’ve had declining new-case rates for the last three weeks. I think that’s a pretty good sign that Omicron is on it’s way out.

That bad news is that Omicron’s easy transmission rate has led to so many more cases that even the lower per-case hospitalization rate has led to more people in the hospital in the Chicago-metro region for Covid than ever before:

This has pushed our ICU capacity to its most strained level yet:

That’s an aggregate number for the whole Chicago-metro region. If you want to know how things are at your local hospital, the New York Times has a tracking site that shows available ICU beds in every hospital, so you can see if your neighborhood hospital would be able to find an ICU bed for you in an emergency (which might or might not be a Covid emergency).

The good news about hospitalizations here is that they seem to have peaked, meaning that area ERs and Covid wards have survived the worst of Omicron and will soon be returning to more normal operation.

The bad news is that the daily death rate also hit an all-time-high of 117/day, and it’s not entirely clear we’re at the peek yet, since deaths always lag the other Covid statistics.

Still, it looks like we may be at or past the worst of the Omicron wave here in Chicagoland (yes, that’s what we call it). There are reasons to suspect this might be the last major Covid wave we will have to endure. Probably not, but I’m hoping.

This post by Mark Draughn at Windypundit was originally published at Covid Stats Dump – 2022-01-29

Public health messaging about this has been terrible. The truth is that not all masks are created equally, and some masks are much better than others. I think public health authorities have been reluctant to say this out loud for a number of reasons, such as not wanting to cause a shortage of high-grade masks and not wanting to discourage people from wearing lower-quality masks if that’s all they have.

I should also acknowledge that the science of mask construction is not fully worked out. It’s difficult to study the effects of masking in the middle of a pandemic when there are so many different types of masks and so many things are changing at once. Scientists have evidence for a lot of effects that public health authorities aren’t comfortable turning into public guidelines.

That being said, I want to start with four important points about masking:

1. No mask offers perfect protection. Even the best filtration materials will allow some virus particles to pass through. Even the best fitting masks will have a little leakage around the edges. No mask will make you completely safe.^[1]That would take a full hazmat suit with air tanks, and even those can be damaged or worn incorrectly.
2. All masks offer some protection. Even the poorest fitting cloth masks can remove some Covid virus particles from the air you breath. All other things being equal, masking never hurts.^[2]But masks with large holes or that don’t cover the mouth and nose aren’t helping either.
3. All masks do a better job protecting other people from you. No matter how well or how poorly a mask protects you from other people who have Covid, it probably does a better job of protecting other people from you if you have Covid. Wearing a mask doesn’t just protect you. It also protects others from you.
4. Even relatively small effects at the personal level can add up across a population. A low-quality mask’s 10% protection may not do much for you, but if everybody wore one instead of going bare, a 10% reduction in the rate of spread throughout a large population for the duration of an infection wave can protect hundreds of thousands of people from Covid and reduce the stress on hospitals.

In other words, even wearing widely-mocked cloth masks such as traditional bandanas and neck gaiters can offer some level of protection to you, the people around you, and the population at large. But if you want to wear a mask that will offer you some serious protection, you can do a lot better.

The key to effectively protecting yourself with a mask is to use one that (a) has an effective filtering material, and (b) forces inhaled air to go through the filter instead of around it. That is, good masking requires the “two Fs,” filtration and fit.

As a general rule, simple cloth masks are going to fail on point (a). Typical woven cloth is just too porous to act as a very good filter. If you can hold it up to a light source and see tiny pinholes where the light shines through, it’s not much of a particulate filter. It might stop Covid in droplet form — as from a sneeze or wet cough — but it won’t do much to stop aerosolized Covid particles floating around a room. More complex mask designs made of several layers of cloth can improve on this a lot, depending on the materials used. I’ve seen studies that suggest a mix that includes things like electrostatic cloth and chiffon can be a great combination, and some cloth masks have a pouch to hold a replaceable filter over the nose and mouth.

Medical-style procedure masks — the rectangular ones we’re used to seeing on nurses and dental assistants — are typically made of non-woven materials that have great particulate filtration characteristics, but they tend to fail on point (b) because they don’t conform to the shape of the face very well. This makes for a poor seal, and air leaks around the edges and up along the gap where the nose meets the cheeks.

The general consensus is that these are better than most cloth masks, but that’s in part because procedure masks are standardized and therefore easy to test. It’s certainly possible that some well-designed cloth masks are actually better.

One solution is to combine the two technologies by wearing a cloth mask over a procedure mask. The anti-mask contingent likes to make fun of this (“OMG, the mask Nazis now want us to wear two masks!”) but the principle is sound: The procedure mask provides excellent filtration, and the cloth mask on top holds the procedure mask firmly against the face to provide a good seal. In studies, some of these appear to provide particulate filtration at least as good as a full N95 mask.

But there’s a much easier way to get N95-quality protection: Wear an N95 mask.

What makes an N95 mask important is that it’s more than just a mask, it’s a respirator. It is intentionally designed and manufactured to provide you with filtered air when you inhale. Obviously, any porous material you place over your nose and mouth will filter the air flowing through a bit — that’s why cloth masks are not totally useless — but respirators are specifically designed for the purpose and made from special materials that provide the necessary degree of particulate filtration. Moreover, approved N95 respirators meet standards of design and manufacture specified by the National Institute for Occupational Safety and Health (NIOSH).

Having said that, please don’t make the mistake of thinking that I’m telling you to wear some fancy medical gear. NIOSH evaluates products for occupational use in general, not for healthcare — that would be the FDA’s job. And before the pandemic, most N95 masks sold in the United States were not FDA approved for medical use. They were sold in hardware stores, and we called them “painter’s masks.”

When the COVID-19 pandemic hit, hospitals began running out of FDA-approved N95 masks, so the FDA issued an Emergency Use Authorization allowing all masks meeting the N95 standard to be used in healthcare for protection against Covid. And for a long time, most N95 masks in this country went to healthcare workers.

A lot has changed over the past two years. Respirator manufactures like 3M and Honeywell activated plans to step up respirator production and they began building out their factories to increase production even further, and a bunch of smaller companies joined in the production of N95 masks. Healthcare workers now have sufficient stockpiles, and N95 masks have become much easier for the rest of us to find (such as this one at Walmart or a whole bunch of them at Grainger). So there’s no excuse not to get an N95 mask if you want one.

Some people question the importance of masking now that we have a vaccine for the SARS-Cov-2 virus. That’s not an unreasonable point, but I have a few counter-arguments:

The vaccine was never 100% effective, so it is best evaluated the same as any other forms of protection — distancing, masking, etc. — and it’s important to consider the trade-off involved. E.g. if the vaccine is 95% effective, and we respond to vaccination by relaxing our other preventive measures so much that infection becomes 20 times more likely, then we will have achieved no net benefit in the fight to avoid catching Covid. Of course, the vaccine also reduces the severity of Covid cases, and we do get a great improvement to our quality of life in other ways — no masks, parties with friends, and so on — which should not be ignored.

However, if you do catch Covid, you might end up transmitting it to other people. That could be especially dangerous if they are unvaccinated, immunocompromised, or have other health problems that exacerbate a Covid infection. Those people thus bear some of the cost of your not masking, but receive none of the benefits. I’m not sure how much consideration you should give to the costs they might pay, but I’m pretty sure it isn’t zero.

Finally, vaccines stop proteins, but masks filter particles. The Pfizer-BioNTech and Moderna vaccines were both about 95% effective against symptomatic Covid caused by the the original SARS-CoV-2 strain. With the Delta variant, effectiveness is somewhere around 88%. The Omicron variant is too new to have good data, but some early studies suggest those vaccines are no more than 20% effective against symptomatic Covid caused by Omicron.^[3]“Symptomatic COVID” is easy to detect quickly, but it tells us little about severity of illness. Lab experiments and some early field data strongly suggest that vaccination with a booster is very effective at preventing all known Covid variants from progressing beyond a bad cold. N95 masks, on the other hand, continue to filter out more than 95% of virus-sized particles, no matter what proteins they’re made of.

(That’s not to say that N95 masks will stop you from catching Covid from the variants. Omicron, for example, seems to multiply much more rapidly in the nose and throat than earlier variants, so even small numbers of virus particles will result in a Covid infection. However, masks are not subject to the escape effect of vaccines, and their relative protection factor remains the same. A mask that made it 10 times harder to catch original Covid will still make it 10 times harder to catch Omicron. It’s just that the baseline for Omicron makes it much easier to catch.)

There are obviously a few downsides to wearing N95 masks.

• They’re masks, and people have a variety of arguments for not wearing masks, ranging from the serious to the speculative to the seriously stupid.
• N95 masks are not reusable. You don’t need to dispose of them after a single use, but they can’t be washed and they do wear out.^[4]There are reusable masks that meet the N95 standard, but they look like big rubbery gas masks because that’s what they are. And you still have to swap out the filters.
• N95 masks are more expensive than non-N95 disposable procedure masks.

For me, none of these are major issues. I don’t wear masks often enough for cost to be a major consideration, and they only bother me for a few minutes until I get used to them. Add to that the fact that I have a comorbidity or two and sometimes spend time with elderly and immunocompromised people, and an N95 mask just makes sense.

Having presented my argument for using N95 masks, let me talk about some choices. The key to getting the full benefit of an N95 mask is to find a model of mask that fits well and forms a good seal against your face. If you had to wear an N95 respirator for your job, you would be required to go through a periodic OSHA-specified fit testing procedure to find a mask that fits correctly. We can’t all do that, but you may need to try several different types of N95 mask until you find one that stays sealed against your face while you move your head and talk normally.

First, however, I should mention the one type of N95 mask you should not wear:

That little square block on the front is an exhalation valve that opens up when you breath out, making the mask less uncomfortable to use. That’s great when you’re using the mask to protect you from dust while sanding drywall patches, but it fails as a Covid-19 mask because it lets your breath escape without filtration. If you’ve caught Covid, this mask will do very little to prevent you from spreading it to everyone you meet. Thus, you want a mask without an exhalation valve.^[5]Many places with strict masking rules will kick you out if you’re wearing one of these.

Now let’s look at some masks.

(Note: There are no affiliate links in this post. I don’t make any money if you follow the links and buy something.)

These top-of-the-line Aura masks are manufactured by industry giant 3M, and hospitals have been using them since long before the pandemic started. They have a soft, comfortable face seal, and the large surface area means they restrict your breathing relatively little despite being made of a material that filters particulates extremely well. They are also known as some of the easiest masks to fit correctly, and they are shipped folded flat, so you can slip a couple in your purse or jacket pockets.

Personally, I find them a little harder to breath through than some other masks, and putting them on correctly is time-consuming — lots of flaps and straps to position correctly. But if I’m going someplace where I know I’ll want a good mask for a long time, this is my current choice.

Note that the mask in this picture is the 3M model 1870+ of the Aura mask, which is FDA approved for use during surgery. You don’t need that. You can just buy a non-surgical version, such as the model 9205+, which you can find at places like Home Depot and True Value.

My personal favorite mask for everyday wear is this 3M model 9010 dust mask:

These are definitely a step down from the Aura, but they fold flat across the vertical center line and are easy to put on: Just hold it with one hand and pull the straps over your head with the other, then shape the nose piece. The resulting mask fits my face well and is comfortable enough for long-term wear.

My favorite thing about these masks is that the filter material is flexible enough to breath in and out as I inhale and exhale. That tells me that I’m producing pressure changes inside the mask, which means it’s sealed tight. If it’s not flexing as I breathe, I keep adjusting it until it does. I get them in 50-packs of individually wrapped masks from MSC Direct.

The Aegle N-95 respirator is another foldable mask that gets great reviews. It’s slightly less expensive than the 3M mask but seems very well made. I personally find them a little hard to fit correctly, but that probably says more about my face than about the mask. Otherwise they would probably be my go-to mask. Available by the box, case, or pallet load, directly from Aegle.

If cost is a big concern, these pouch-style respirators from Kimberly-Clark get good reviews and still cost less than $1 per mask in packs of 50. They used to be less than 50 cents per mask, but like many N95 masks, the price seems to have gone up with the Omicron wave. Not my favorite fit, but people with more normally-shaped heads than mine seem to like them.

Another type of N95 mask I like, at least in theory, is the SoftSeal N95, available in cup or folding shape. These masks have silicone gaskets around the edges to provide a soft, flexible seal against the face. Although they don’t quite fit my face, other people swear by them, and I think flexible seals are definitely the right idea in long-term mask wear. The ones pictured here have the dreaded exhalation valves, but you can get them without exhalation valves directly from SoftSeal.

I should say something about KN-95 masks. These are usually described as the Chinese equivalent to the American N95 mask. That’s mostly true, but they differ from N95 masks in one fundamental way: They use ear loops instead of head straps, and thus they don’t hold the mask as tightly against the face. They also don’t technically meet the N95 standard, although for a while the FDA approved them for pandemic use. That approval has been revoked in healthcare settings — in part because of massive counterfeiting operations — but they are probably good enough for non-medical use.

I wore these Powecom KN95 masks for months before I was able to find decent N95 masks online. Like the 3M 9010, they breath when I breath so I can tell when the seal is good, and they are easy to put on and take off. My wife swears by them. They seem less likely to be counterfeit than some other brands, and you can get them in packs of 10 at BonaFideMasks.

Finally, just for fun, I should probably mention the AirGami mask:

The Airgami mask uses oragami-like folding techniques to shape the mask, and they are available in a variety of colors, patterns, and sizes, with either head straps or ear loops. Everything about the Airgami website implies that they are almost, kinda, sorta N95 masks that will be NIOSH-approved any day now… but they aren’t actually on the NIOSH Certified Equipment List.

That doesn’t mean they’re a ripoff. I’ve seen several companies that have started making masks which meet all the N95 requirements but haven’t yet received the official stamp of approval from the government. In Airgami’s case, they even have a report from a third-party testing company showing that they meet the N95 standard (presumably for the headstrap version).

Furthermore, I’ve seen twitter reviews by doctors who swear that these masks are very comfortable for long-term wear. They sound like a great modern take on the N95 mask, and even without NIOSH certification, the reviews make me want to try them out.

Except for one thing: They cost over $20 per mask! They’re supposed to be reusable, and they can be disinfected with steam or in an oven, but damn.

Finally, I should include a few notes on how to use N95 masks.

The melt-blown particulate filter material does a great job of cleaning the air, but only if all the air actually passes through the filter material. That only happens if the mask is fitted snugly to your face and has no leaks anywhere around the entire edge of the mask. In an occupational setting you would get help from a trained expert. For personal use, you will just have to make do.

(It’s not rocket science, and the worst that can happen is that it will function no better than a procedure mask, so don’t sweat it too much.)

The most important thing is to follow the manufacturer’s instructions for donning the mask. If instructions don’t come with the masks you bought, check the manufacturer’s website.

In the event you can’t find the instructions, the donning procedure is generally something like this:

• Sanitize your hands.
• Take the mask out of its container and inspect it for damage.
• Open the mask up and find the upper and lower straps.
• Holding the mask in front of you, pull the straps over your head.
  • The lower strap should go below your ears and around your neck just below the base of your skull.
  • The upper strap should go above your ears and around the back of your head.
• Adjust the mask to fit:
  • Using both hands, one on each side, shape the metal piece over the top of your nose to hold the mask firmly against your nose and cheeks. (Every manufacturer warns against trying to use just one hand.)
  • Adjust the positions of the straps to pull the mask into a snug fit against your face at all points around the edge.
  • Untwist the straps so they lie flat against your head.
  • Conduct a seal test by covering the front of the mask with your hands and exhaling. Check for air escaping around the edges of the mask.
  • If the mask doesn’t fit, repeat these adjustments until you are satisfied.

One more note, just for the guys: If you want to use an N95 mask, it’s probably best to shave. Even a slight beard can impair filtering efficiency by keeping the edges of the mask from making smooth contact with the skin, and anything over 1/8 inch will likely drop the mask effectiveness below its specifications.

That’s it. I remind you once again that I am not a PPE expert, merely a PPE enthusiast, and if you see any dangerous mistakes, be sure to let me know.

Good luck out there.

This post by Mark Draughn at Windypundit was originally published at N95 or Bust!

Two weeks to slow the spread.

That was the original rationale for the lockdowns, masking and social distancing: Prevent transmission of the coronavirus so that Americans could be assured that we would not overwhelm hospital capacity, causing needless death.

The “two weeks to slow the spread” concept was from March of 2020, back when we knew almost nothing about COVID-19. All we had was news of the outbreaks in Wuhan, China, where it had apparently been contained^[1]If we believe China. and in Lombardy, Italy, where it exploded through the population, overwhelming hospitals and killing lots of people.

Making matters worse, the CDC and the FDA had screwed up our disease surveillance for COVID-19, so we had no good information about how the virus was behaving here. All we knew was that (1) we were past the point where we could manage it with testing and isolation, (2) all our numbers — cases, hospitalizations, and deaths — were doubling every few days, and (3) we didn’t want to be the next Lombardy. So we had few choices other than hunkering down to suppress the wave.

(And even then there were pundits panicking that we were committing “economic suicide,” a fear which has proven unfounded by subsequent economic developments.)

Wait until a vaccine is available.

That was the next goal post: an admonition to continue to take precautions to avoid spreading the coronavirus until a vaccine could be developed. […]

Wait until every adult has a chance to get the vaccine.

That was the final rationale for caution. […]

And yet.

We are told that we are experiencing a massive COVID-19 crisis. We have been told that the vaccinated must mask up again; that the unvaccinated should be barred from public establishments; that children must be masked in school.

This is disingenuous. Shapiro is trying to paint a picture of moving goal posts — public health officials using ever-changing criteria to keep keep enforcing their petty rules. But that’s not what happened.

For one thing, the “two weeks” figure was from a Trump White House press event. Few public health professionals believed it could be that short. And though the lockdowns lasted longer than two weeks, they were gone within a few months, and most places haven’t gone back to restrictions that severe.

That lockdown period gave healthcare professionals and hospitals time to learn better ways to manage Covid patients — remdesivir, dexamethasone, prone positioning, better ventilator protocols, and so on.

(Then there’s Shapiro’s cheap trick of counting “Wait until a vaccine is available” and “Wait until every adult has a chance to get the vaccine” as two separate things.)

As for Shapiro’s mock mystification about the continued public health concerns, the answer is pretty simple: Between the time the vaccination program started and now, several of the COVID-19 variants have begun to spread widely, especially the much more virulent Delta variant.

Vaccinated people can and do catch the Delta variant, in higher numbers than for the original SARS-CoV-2 virus on which our vaccines were based, and they can then spread it to others. We may have about half our population vaccinated, but the Delta variant is about twice as likely to break through a vaccinated person’s immunity, and within unvaccinated people, it seems to spread at least two or three times faster than original COVID-19. So while vaccinated people are largely protected from serious illness, the unvaccinated population is much worse off.

The statistics simply do not bear this out. According to the seven-day rolling average as calculated by The New York Times, fewer than 400 Americans per day are dying of COVID-19; at the height of the pandemic, well over 3,000 were.

I have the advantage of writing this three weeks in the future. Since Shapiro wrote that, the 7-day average death rate has risen about 150% to 1295 per day. The new case rate has gone up 42%, hospitalization rates are up 56%, and ICU hospitalization rates have gone up 65%.^[2]I’m using data from Covid Act Now, so my numbers differ slightly from Shapiro’s.

The current delta variant spike has resulted in a massive case count, particularly in Florida, but deaths are not following cases —

Stop!

Deaths always lag behind cases, but the death rate is still going up. On July 1, the 7-day average Florida Covid death rate was 30/day. By the time Shapiro’s column was published in August 8, it had already nearly tripled to 88/day, and since then it’s nearly tripled again to 246 per day. That’s an eight-fold increase in less than 2 months.

Every time we’ve been hit with a new wave of COVID-19 cases, some people have tried to use the initial low death rates to minimize the threat. It’s true that this time, for the first time ever in the pandemic, there’s a solid scientific reason — vaccination — to believe deaths will be reduced. But until we’ve seen the whole wave of deaths, it’s too soon to declare victory.

Those who are vaccinated are not dying of COVID-19; their death rate is minuscule. Those who are unvaccinated have chosen not to vaccinate; they are independent adults capable of determining their own approach to risk and reward.

I’m not comfortable dismissing the harm to the unvaccinated. Being unvaccinated isn’t always a choice: Children aren’t allowed to get the vaccine, some people have allergic reactions, and some people have compromised immune systems, so the vaccine does little for them.

Furthermore, most of the remaining unvaccinated people are not anti-vax nutcases. Many are decent people who have concerns about some aspect of the vaccine they don’t understand. Many of them are confused or misinformed. often because they have been deliberately misled by the aforementioned anti-vax nutcases. These people do not deserve a serious illness or death just because they are uncertain, confused, or the victims of disinformation.

Even if you still think we should dismiss the fate of unvaccinated people, please remember that some vaccinated people, including the old and vulnerable, can catch COVID-19 from unvaccinated people, and some of those vaccinated people will get very sick and some will die. So if the new case rate grows ten-fold, as it has since June, then vaccinated people will be exposed to 10-times as much Covid, resulting in an increase in breakthrough cases, hospitalizations, and deaths.

Finally, although SARS-CoV-2 does not mutate terribly fast, it does occasionally spin off mutant variants, and the more people who have Covid, the more chances there are for mutant strains to arise. Thus the more likely we are to face additional variants, some of which could be faster spreading, deadlier, or able to escape vaccination.

Unlike other behavioral health problems, such as smoking or obesity, COVID-19 is contagious, which means no one is making decisions just for themselves.

All of which requires us to ask the question: When are we done?

When are we done telling children to mask up to protect adults who don’t want to vaccinate? When are we done telling businesses to close up or bar customers based on vaccination status? When are we done with mask mandates (data suggests that mask mandates are ineffective, even if masking is sometimes useful), with evidence-free social distancing rules (six feet is pure conjecture), with the ever-vacillating, Delphic pronouncements of Dr. Anthony Fauci? We have hit the goal posts; every adult now has the capacity to protect himself. There are no other realistic goal posts: Zero COVID-19 cases was never a realistic goal.

When is the job of government done?

And yet.

Our public health “experts” continue to promote more and more outrageous restrictions. […] There is no limiting principle to this, no end goal. There is only a bureaucratic and political elite unwilling to treat citizens as adults, recognize their own limitations and leave us all alone.

This is a variation on a common argument: We can’t do anything effective about Covid, they say, so we might as well accept the risk of Covid and go back to normal life without restrictions.

That argument wouldn’t piss me off nearly as much if many of these same people hadn’t been reaching the same conclusion over and over again at every stage of the pandemic. They proclaim that we should go back to normal and denounce anyone who says otherwise. Hundreds of thousands of Americans have died since the first time I heard that argument. And it’s a bad argument, because accepting the risks of Covid doesn’t look like they think it does.

Let me see if I can explain…

Imagine you’re driving through a forested area in a large national park. You see something interesting through the trees and pull over. You get out of the car, grab your cotton hoodie to fend off the slight chill, and walk into the woods to get a closer look. Maybe you find what you’re looking for and take a few pictures, or maybe you don’t. Either way, you eventually head back toward where you parked the car.

After walking for several minutes, you feel like you should have reached the car already. You press on a little further, and still don’t come to it. You look around, and you think maybe the uneven terrain has caused you to curve to the left a bit, so you turn right and head off in that direction, hoping to intercept the road. After about 45 minutes, you’re still in the woods. Maybe you got turned around. The sky is overcast, so you can’t navigate by the sun even if you could see it through the canopy. You decide to go back the way you came, hoping to find where you took the wrong path. maybe something will look familiar. Two hours later, you’re still lost, and the sun is starting to go down. The air is getting colder as night falls.

What happens to you next depends a lot on your ability to accept an important conceptual change in circumstances: You are no longer a person trying to find your way back to your car. You are now a person trying to survive the night in the deep forest. You need to stop thrashing around wasting energy and sweating into your clothes and start thinking about finding shelter and maybe starting a fire.

If this stretches into the next day and beyond, you may find yourself needing to accept yet another conceptual change: You are no longer trying to survive in the forest. You are now trying to live in the forest, meaning you need to find water and food.

As your situation becomes increasingly perilous, you need to accept the new reality and change your behavior to deal with it realistically if you want to survive.

The same principle likely applies to the COVID-19 pandemic: Our situation has changed, and we need to change our behavior to deal with it. Or to put it another way: Shapiro and others may be right that we will have to learn to live with Covid, but maybe what we’re doing now is what that looks like.

I’m not saying the solution to endemic Covid will be exactly the policies we’re following today — because there’s a lot of stupid stuff going on in both directions — but if we’re still living with Covid five years from now, our lives are going to have to adapt to the new reality.

It may seem drastic to alter our lives so much, but I contend that it only seems drastic because we’re not thinking in the proper historical context. We’ve already altered our lives to mitigate many other risks, but some of those adaptations have been baked into our lives for so long that we don’t normally notice them.

For example, we have a lot of adaptations to guard against diseases:

• The water we drink is processed and filtered by gigantic water treatment plants, except for people who have their own wells, because they they have smaller filtration systems of their own. The water moves through our cities and houses in sealed systems that keep it separated from sources of contamination.
• We have systems for dealing with waste water too: It’s dumped into sceptic tanks or drained away in massive city-scale sewer systems, and it’s processed before being released to the environment. This is our normal life in a world with waterborne diseases like typhus, cholera, and dysentery.
• Almost every single house has a refrigerator that allows occupants to store foods for longer periods without spoiling. We likely bought those foods from refrigerated display cases at grocery stores, and the foods arrived at those stores in refrigerated trucks, and may have been transported in refrigerated shipping containers.
• We also have stoves, which allow us to cook food to kill pathogens. Or foods may be heated to safe temperatures in food preparation plants and then sealed in cans or bottles to prevent contamination. Once the sealed containers are opened, we serve the food immediately or refrigerate it to prevent disease.
• Restaurants follow all of these practices for handling food and water, and ten times more. They pile on tons of additional processes, procedures, and equipment for preventing food contamination, including sneeze guards, gloves, cleaning chemicals, and appliances for holding foods at appropriate high or low temperatures.

Outside the realm of disease, we go through a lot more trouble to protect ourselves against danger:

• We build fully enclosed and sealed homes to protect ourselves from weather and animals.
• We have heating and cooling systems to protect us from extreme temperatures.
• We have locks and latches and alarm systems to protect us from intruders.
• We put an enormous effort into making sure building materials resist fires.
• We protect against the hazards of electricity with things like circuit breakers, conduit, electrical boxes, ground fault circuit interrupters, arc fault circuit interrupters, polarized outlets, and grounded appliances.
• Cars have dozens of safety systems such as headlights, marker lights, windshield wipers, tubeless tires, dual brake systems, rounded and padded interior surfaces, anti-burst door locks, seat belts, air bags, ignition interlocks, and crumple zones…
• Commercial aircraft have multiple redundant systems, and crews are trained to deal with a variety of emergencies from fires to turbulence to water landings.
• As I write this, Hurricane Ida has made landfall in New Orleans. Buildings have storm shutters on their windows, and the whole city is protected from flood by a system of levies. Thousands of people were evacuated in advance, and rescue and relief personnel are standing by with supplies.

I don’t see how adapting our lives to a new risk like Covid is in principle any different from all those other safety measures we live with every day.

To be clear, I’m not talking about doing exactly the same things we’ve been doing for the past 18 months. We were taken by surprise last year, we were at the beginning of the learning curve, and there was a lot of bad information from both official and non-official sources. We’ve thrashed around a bit finding answers, but I assume we’ll get better at this.

Let me try my hand at imagining what a mature, well-developed plan for dealing with COVID-19 might look like^[3]Please remember that I am not an expert on this subject, so this is at best some informed speculation.:

• Vaccines will do most of the work. If it turns out to be necessary, we should aim to produce enough vaccine to support periodic vaccination and/or booster shots, like we do with the flu vaccines every year, possibly even combined with the flu vaccine.
• If more dangerous variants come along, we should make new vaccines that target them.
• We should improve air filtration and/or fresh-air exchange in the buildings we live and work in, so that aerosolized COVID-19 cannot build up when the buildings are occupied. This needs to happen ASAP for some buildings, but others can probably wait. I imagine better ventilation and filtering will be part of most new construction eventually.
• We should have a standing COVID-19 surveillance program, just like we do for other diseases, so that we have a good idea what the virus is doing and can quickly spot outbreaks.
• We need to make testing easier and more available, especially at-home rapid testing.
• We need better masks. Everyone should be able to get masks that offer protection comparable to an N95 mask, but which are more comfortable, more reusable, easier to don and doff, and more attractive. The technology is relatively easy, but we will need to revise regulations on masks so that sellers are able to accurately communicate their capabilities to buyers.
• When COVID-19 outbreaks and flare-ups occur, we should be ready to respond with appropriate combinations of mitigation steps. These could include:
  • As always, wash your hands.
  • Massive testing, to spot outbreaks before they infect too many people.
  • Contact tracing, to identify the causes of the outbreak, and therefore how to mitigate it.
  • Community masking, for source control and personal protection.
  • Social distancing rules, including, if things get really bad…
  • Partial lockdowns, intelligent ones, informed by the latest scientific studies, and based on a good understanding of how Covid is spreading.

With planning and preparation, we ought to be able to implement most of these mitigation steps without a lot of disruption. And in a world where we occasionally evacuate tens of thousands of people for hurricanes and wildfires, we should be able to implement even as severe a mitigation as a partial lockdown without more pain than necessary. And if the levels of mitigation responses are pre-planned with a clear understanding of the triggering criteria, people will be able to plan ahead. It may even be possible for insurance companies to estimate the risks well enough to offer some kind of lockdown insurance.

We may not ever be able to go back to the way things were, but with technology we already have, or could easily develop, we should be able to get to a place where we really are living with Covid and managing it as just one more health risk among many.

This post by Mark Draughn at Windypundit was originally published at Living with Covid is like being lost in the forest

CovidActNow

If you want a one-stop snapshot of how the pandemic is going, start at CovidActNow. They don’t have a lot of fancy data tables and charts. Instead, they boil all that down into some simple color codes.

The colors follow a fairly standard green-yellow-orange-red progression, with dark red added late last year to represent the awfulness of the winter surge. This coding system was developed by a group of experts in an effort to find a way to communicate regional COVID-19 conditions in a simple way. You can also get a look at 5 key metrics for any state or county. For example, here’s Kentucky:

Kentucky is coded red because with 35.9 new cases per 100,000 residents, Covid is still quite active (although cases would have to more than double to hit dark red). It will turn orange when cases drop below 25 per 100,000 per day, then yellow at 10/100K/day, and finally green when only one person in 100,000 gets Covid on any given day. (These risk levels thresholds were developed by the Harvard Global Health Initiative).

On the other hand, the infection rate of 0.83 is pretty good news. Infection rate — you’ll sometimes see it called R_t — represents the average number of people who will catch Covid from an infected person. At values greater than 1.0, it means that one infected person passes the infection on to more than one additional person — replacing themselves, and then some — so the number of infected people is increasing exponentially.

With an infection rate less than 1.0, each infected person is unlikely to infect someone to replace them after they recover. It’s sometimes easier to think about it in terms of a population: If 1000 people are infected, an infection rate of 0.83 means they are expected to pass the disease on to 830 more people, who will pass it on to 689 people, and so on. Eventually, only 1 person will get it, and they won’t pass it on, and Covid will be eradicated. At 0.83, that will take a long time, but at least it’s not getting worse.

The positive test rate, a.k.a. positivity, is a measure of testing adequacy for the level of cases the region is seeing. Anything over 20% likely means there isn’t enough testing and you really have no idea how many cases you have. Below 20%, positivity is also a good measure of whether the infection rate is growing or shrinking, independent of the number of tests being done. When this number is small enough, probably around 3% according to most experts, it means your area has enough testing to rapidly find the majority of infected people. And trace them too, if contact tracers have been hired.

ICU capacity coding indicates whether your hospital system is in danger of being overloaded if your region is affected by a surge of Covid cases. Occupancy of 68% is normal for most hospitals, and they can easily absorb a brief surge of Covid cases. However, if the surge is prolonged, and occupancy hits 85%, a continued surge will likely overwhelm them and force them to make tradeoffs. On the other hand, many hospitals have plans to do this as carefully as possible, and as far as I know, no U.S. hospital has been so overwhelmed as to have to make decisions to let some patients die.

The vaccination reports are a new metric, but there’s no color code as yet, probably because there’s no obvious way to set thresholds until we have more information.

The local regional pages also have detailed historic data on several of the metrics (so yes, they do have some fancy charts and tables). There’s also some educational material, including an explanation of the rationale behind all the metrics. And there are also some tools, including an API and embeddable code. As I write this, I’m using the latter to display Illinois gating statistics in the sidebar of this blog.

TL;DR: CovidActNow provides a simple breakdown of the state of the pandemic. And if all goes well, over the coming year we will get to watch all of those states turn green. And never go back.

Big Stats

Several sites offer massive amounts of Covid statistics. Everyone is probably already familiar with the Worldometers Covid page, which allows you to see a snapshot of current statistics throughout the world or focused in on the United States. If you prefer more graphical pizzazz, and a better science pedigree, there’s the Johns Hopkins Coronavirus Resource Center map.

Another good data site is 91-DIVOC, which offers impressive visualizations of Covid statistics, such as this chart of new confirmed cases by day, per country, normalized by population.

The actual on-site visualizations are interactive. You can see in this screen cap that I was hovering over the U.S. data series on December 30. You can tweak and adjust these to display a variety of different data series with different presentations.

Another site which I’ve just started to explore is the Carnegie Mellon Delphi Group site, which has a lot of health surveillance data, for U.S. states and counties, such as mask wearing percentages, reports of Covid-like symptoms, and mobility data such as time spent away from home and in bars or restaurants.

TL;DR: These sites are data geek playgrounds, offering lots of raw data, charts, tables, and APIs.

I would be remiss in not mentioning one of the earliest sites I used, the Covid Tracking Project. They’re a rag-tag bunch of volunteers that came together to create one of the definitive sources of Covid statistics, relied on by epidemiologists and public health officials throughout the country. Alas, they are shutting down operations in March. They formed to fill the gap created by the lack of good data from the CDC and HHS, but now government sources are finally catching up, and they feel their efforts are no longer necessary.

The CDC

Speaking of government sources, the CDC’s Covid Data Tracker site seems to be adding new information all the time. In addition to the usual stats, like vaccination statistics, a cases and deaths snapshot and the associated trend data, they also have demographic statistics, seroprevalence survey data (measuring the percentage of people with Covid-19 antibodies, presumably because they have been infected) and a geographic pandemic vulnerability dashboard.

One of the things that sets the CDC data apart from the other data sources is that they curate and clean their data carefully. When a public health department revises its data, the CDC revises theirs. If there are reporting glitches or gaps due to missing or misreported data, the CDC data usually fills them in and smooths them over in a way that’s epidemiologically sound. That does tend to delay the CDC data compared to most other sources, but it’s good data.

Finally, for months now, HHS and the White House coronavirus task force have been producing semi-secret weekly COVID-19 State Profile Reports which they have been sharing with state governments, but not with the general public. Those state reports are now available, along with a nation-wide report). These reports are densely packed with terrific data — so terrific that I really don’t know how to use most of it. This stuff is aimed more at public health professionals than people like me.

TL;DR: Government sources are now vastly improved, and the CDC is probably the best source of data.

Models

We all want to know what’s going to happen next, and there are a ton of people running models to try to tell us what COVID-19 will do next.

(Technically, I’ve already showed you a model or two since R_t , a.k.a. infection rate, is a theoretical value that has to be fitted from data.)

There are now so many models that it’s hard to pick any of them, so maybe you’d like to see a bunch of them? Nate Silver’s FiveThirtyEight statistics website has a brief summary of how a bunch of popular models differ and what they are currently predicting. The prediction charts aren’t that useful, especially since they show cumulative values, and in the near-term we’re more interested in daily changes.

Once you’ve read the educational material at FiveThirtyEight, you can see more technical presentations of the model outputs at The COVID-19 Forecast Hub. For example, here is the U.S. ensemble prediction for new cases for each of the next four weeks:

(Note that the figures are per week, not per day.)

This ensemble forecast shows the point value prediction and the 95% confidence interval for a weighted combination of the case rate prediction of all the models combined. You can also display predictions for weekly or cumulative deaths, and you can choose which models you want to see.

The models differ in which data sources they use, the methodology used to make predictions, and most importantly, how they incorporate changes in human behavior. For example, some models assume that current rates of social distancing, masking, and indoor gathering will continue throughout the prediction period. Others make assumptions that people will change their behavior (and government will change their rules) based on the increasing or decreasing severity of the epidemic. This can lead to wildly different predictions, all of which may be valid under their assumptions about various unknowns.

TL;DR: The models are interesting, but there are so many of them.

Miscellaneous

The New York Times has a tracking board for vaccine development, with summary descriptions of the current state of each vaccine candidate and links to news articles.

The NYT also has a similar tracker for COVID-19 drugs and treatments.

Bloomberg has a nice overview of vaccine distribution and administration, with a combination of news, data, and flashy graphics.

If you want to fiddle with the data yourself, here’s one handy list of APIs for Covid information.

Finally, for a different kind of model, check out the microCOVID Project, which is designed to help you estimate your personal chance of catching COVID-19 from various activities. The creators want to encourage us to think about risk in terms of a “microCOVID” — their word for a 1-in-a-million chance of catching COVID-19. For example, if I spend 3 hours hanging out with a friend from the area, indoors, with both of us wearing surgical masks, that’s about 100 microCOVIDs. But if I spend those 3 hours at an indoor party with 10 people from my area, with no one wearing masks, the microCOVID site scores that at 9000 microCOVIDs.

Personally, I don’t find the microCOVID concept intuitive. I end up converting it to a fraction or a percentage. So spending 3 hours with a friend carries 1/10000 chance of of getting COVID-19, but spending that time at the party carries a nearly 1% chance of catching COVID-19.

This post by Mark Draughn at Windypundit was originally published at Some Useful Sources of COVID-19 Data

The thick orange line is a 7-day moving average of the test positivity, with a fainter orange line showing the actual daily reports of test positivity. The three dashed horizontal lines are positivity targets set by various organizations.

• The top line, at 8%, is the target used by the Illinois Department of Public Heath for setting re-opening rules.
• The middle line, 5%, is a target recommended by the CDC for adequate testing.
• The bottom line, 3%, is the target where the Covid Exit Strategy think tank believes that public health measures (test, trace, isolate) can suppress the disease.

So, I calculated the main positivity data line directly from testing data I pulled from the Covid Tracking Project, whereas the more theoretical target lines are based on calculations, models, and rules of thumb created by professionals in the field.

Recently, I’ve started posting time-series charts of vaccination data, and I’ve found they don’t tell me what I really want to know, which is how much of the U.S. population is now immune from COVID-19. I think I can make an estimate of that, but it’s not a simple calculation, and there are some assumptions.

In other words, it’s a model. And I figured I should document how I’m calculating it.

For my purposes, people are immune from the COVID-19 virus in one of three ways:

• Natural immunity, from having caught and recovered from COVID-19.
• Partial vaccination immunity from the first dose of vaccine.
• Complete vaccination immunity from the final dose of vaccine.

This is a super-simple model that only calculates a point estimate — I have no idea what the error range is. Here’s my latest immunity chart for the entire United States:

As you can see, only about 1% of U.S. residents are immune from having completed vaccination. The downward move at the end occurs because some states adjusted their reporting.

Methodology:

The simplest calculation is the number of people who are immune from having completed vaccination. I calculate the number of completely vaccinated people as the number of people who received their second dose, lagged by 7 days to give immunity time to develop. I then multiply by 95% to adjust for vaccine efficacy to get number of people immune from completing vaccination.

Calculating the number of people immune from partial vaccination is similar. I use the number of people who received the first dose, lag it by 10 days to give immunity time to develop, and then multiply by 46.5% (the average single-shot efficacy reported from Israel) to get the number of people immune from partial vaccination. For display purposes, I adjust that by subtracting the number of people who are immune from completing vaccination.

Finally, I calculate the number of infected people. Since COVID-19 testing was inadequate for the first few months (and perhaps a few times afterward) I calculate the number of infected people by working backward from a less ambiguous number: The number of dead people. I assume an Infection Fatality Rate of 0.65%, meaning that about 0.65% of people who catch COVID-19 die from it, and then I divide that into the number of deaths to estimate the infection rate. I assume that the average death occurs 19 days after the date of infection. If that turns out to be less than the number of people who tested positive, I use the positive test count instead. Then I assume that everyone who has not died by day 22 is going to recover and will be immune by then. This gets me the natural immunity figure. In the absence of better data about reinfection, I assume that 100% of recovered COVID-19 victims are immune.

I assume that people who’ve had COVID-19 receive the vaccine at the same rate as the general population, and I adjust for the overlap by deducting vaccinated COVID-19 recoverees from total recoverees, essentially assigning their immunity to the vaccine rather than natural immunity.

This post by Mark Draughn at Windypundit was originally published at The Windypundit Immunity Model

For one thing, the United States is doing well compared to other countries. In terms of the raw number of vaccine doses administered, we’re leading the world:

As with other Covid stats, that’s skewed by the fact that we are one of the larger countries. A more accurate picture is given using per-capita figures, but even there, we’ve got the fifth best dose administration rate:

Israel, the UAE, and Bahrain are small countries with simple healthcare systems, and the U.K had a bit of a head start, so we’re actually doing a relatively good job of getting the vaccine out.

I’m not bringing this up to brag about American exceptionalism — the United States has little to brag about when it comes to Covid-19 — but because it suggests that there isn’t anything unusually wrong with U.S. vaccine distribution. Everybody is having problems getting the vaccine out to the population. This suggests that the difficulties we’re having in the U.S. are not because the people running the distribution system are failing, but because the problem of rolling out a pandemic vaccine is harder than everybody thought it was.

That makes sense to me, because we’ve never distributed vaccines like this before. (Not lately, anyway.) Normally, we get vaccinations at our doctor’s offices, at walk-in clinics, or at pharmacies. The Covid-19 vaccine doses are being given out to hospital staff at hospitals and nursing home residents in nursing homes, and that’s a logistics chain we’ve never used before. We shouldn’t be surprised that it’s going slowly, because we’re still learning how administer a vaccine that way, and it may simply be harder to do for a variety of administrative and practical reasons.

I suspect that once the general rollout starts, and vaccine doses are distributed through normal and well-understood logistics channels, a lot of people will be vaccinated very quickly.

In fact, my gut feeling (and I could certainly be wrong) is that since we are producing vaccine doses faster than we can get them to high-priority recipients, which leaves us with a significant stockpile of doses, it might make sense to start the general vaccine rollout right now, simply to get the vaccine out to as many people as possible as fast as possible.

This post by Mark Draughn at Windypundit was originally published at The Vaccine Rollout is OK

Before doing that, I need to set some context for the study, which means I need to discuss some of the other research on mask wearing. At the time I wrote my series on masking, I relied on general public health advice, one or two influenza studies, and on a recent CDC post on community masking which summarized a bunch of research that I’m going to discuss in more detail here.

Note: This is not a thorough literature review. In most cases I only skimmed the papers to learn what they had to say about relevant masking issues. Despite that, I should warn you that, even by my standards, this is going to be tedious slog. If you just want to know about the Danish study, feel free to skip to the end.

Overview

The term community masking refers to the practice of a general group of people — a town, a country, an office building — wearing masks to prevent the spread of a disease. This is in contrast to masking in a healthcare setting, which us usually intended to reduce the risk of disease transmission in very specific situations, such as a surgical procedure. Masks have a long history of use in healthcare settings, and are widely considered to be effective there. But the effectiveness of general community masking is less well established.

Respiratory infections like Covid-19 can be carried through the air from person to person by two different mechanisms:

• Droplets: Blobs of liquid expelled as people exhale — or talk or cough or sneeze — which are large enough to settle to the ground within a few seconds.
• Aerosols: Tiny bits of particulate matter that are small enough that they can float in the air for minutes or hours.

(Non-airborne infection can also occur through direct contact or — rarely for Covid-19 — contact with contaminated surfaces.)

Broadly speaking, mask materials may capture particulates from the air using two important mechanisms:

• Sieve effect: The fibers of the mask have gaps between them, but any particle too big to fit through the gap will be trapped by the mask. Most materials provide some of sieve filtration.
• Stickyness: Particles that fit through the gaps between fibers can end up sticking to a fibers through one of several different mechanisms (e.g. electrostatic cling). Only certain special materials provide this kind of filtration.

Wearing masks can serve two roles in infection control:

• Source control: Prevents you from infecting others. If you are infected, covering your mouth and nose with a mask may reduce the amount of exhaled infectious droplets and aerosols you release into the environment, which could infect others.
• Protection: Keeps you from being infected. By covering your mouth and nose, a mask may reduce the amount of infectious droplets and aerosols you inhale, which could keep you from being infected.

For my purposes, we can break the CDC’s list of studies of community masking into two broad categories:

• Lab experiments, which test the mechanisms by which masks are presumed to control infections, but don’t actually show that community masking works.
• Observational studies, which look at events in the real world and try to detect if masking is helping.

Laboratory experiments can test all types of infectious materials, filtering mechanisms, and roles. Observational studies of community masking tend to combine the effects of mechanisms, and usually roles as well, because broad population studies are better for figuring out if masking is working than figuring out why.

Lab experiments are highly controlled to eliminate complications and uncertainties. Healthcare settings are more complicated, but the participants are professionals and are usually subject to direction from management or authorities. Out in the general community, however, people won’t always do what you want them to do, which can make the results a lot harder to interpret. Things that work well in the lab may work poorly in real life.

This doesn’t mean lab experiments are unimportant. Most real-world studies are observational, meaning the experimenters gather data about variables in the the real world and try to use statistics to establish that changes in some variables (mask/no mask) cause changes in other variables (infected/not infected). The problem is that statistics alone cannot establish this — correlation does not prove causation — but lab experiments can identify possible causal mechanisms, which can be used to predict effects which observation can then confirm. This doesn’t prove that changes in some variables cause changes in others, but it does make it more plausible, especially in the absence of other explanations.

Finally, while compliance is important to epidemiologists, it need not be important to us. An observational study on masking may find the effect is small because most participants don’t wear masks when they’re supposed to. But that should have no bearing on your decision of whether to wear a mask. That only depends on if it works.

Lab Experiments

Lab experiments test masking technology under highly controlled conditions.

Mask Materials

This group of experiments examine the effectiveness of various mask materials at filtering airborne particulates and/or droplets.

Simple respiratory protection–evaluation of the filtration performance of cloth masks and common fabric materials against 20-1000 nm size particles

In this 2010 study, conducted after the bird flu and H1N1 pandemics, researchers used microscopic salt particles of various sizes to test 3 variations of each of several materials, including cloth masks, T-shirts, sweatshirts, towels, and scarves. The cloth masks reduced penetration anywhere between 3% and 60%, depending on the material and particle size. Thicker materials generally did better. Smaller particles penetrated better in most materials. This indicates that most filtration is like a sieve, with no other capture method contributing.

Aerosol Filtration Efficiency of Common Fabrics Used in Respiratory Cloth Masks

This 2020 study is similar to the previous one, using different fabrics and particle sizes. Fabrics with tight weaves such as 600 thread/inch cotton produced high levels of filtration by sieve effects. On the other hand, materials such as silk, chiffon, and flannel provided some electrostatic filtering as well. For example, 80 thread/inch quilter’s cotton filtered only 9% to 14% of particles, but a combination of layers of tightly-woven cotton and chiffon filtered at least 97% of particles.

Measurement of filtration efficiencies of healthcare and consumer materials using modified respirator fit tester setup

Yet another salt test of filtration efficiency, this time focusing on do-it-yourself masks. This was also a demonstration of how to test masks using respirator fit testing equipment that is readily available in most hospitals. (It’s a bit of a mad scientist arrangement — for example, they can’t get readings directly from the particle counter software, so they use optical character recognition to read it into MATLAB.) They found filtering efficiencies of consumer-grade materials between 35% (pillow case) and 50% (HVAC filter) although cotton and coffee filters did much worse, and vacuum cleaner bags scored 82%.

Community Masks During the SARS-CoV-2 Pandemic: Filtration Efficacy and Air Resistance

This was a study of a variety of masks obtained from manufactures in and around Germany in 2020. They found a range of filtration efficiencies, from 34.9% for a Hermko 9920 to 99.8 for an Eterna FFP (whatever those are).

Household Materials Selection for Homemade Cloth Face Coverings and Their Filtration Efficiency Enhancement with Triboelectric Charging

Another study using salt particles on common materials — cotton, polyester, silk, nylon, paper towels, etc. — with measurement of pressure drop across the air stream to compute a common quality measurement of particulate filtration efficiency weighted for breathability.

The study also tests the idea of rubbing the mask material with a latex glove to give it a static charge. That improved filtration efficiency for every material except cotton, which got worse. The best filtration was from a charged spunbond polypropylene (which doesn’t sound like a household material, but is apparently used in things like mattress covers and hygiene products) which filtered 10% to 20% of particulates per layer with relatively good breathability.

Filtration performances of non-medical materials as candidates for manufacturing facemasks and respirators

This test used nebulized salt water as a source of aerosolized droplets to test 43 different materials. High thread count fabrics did OK, and fibrous materials (such as HVAC filters) did well collecting aerosols. The recommend manufacturing well-fitting masks from a mix of fibrous and fabric materials.

Viral Filtration Efficiency of Fabric Masks Compared with Surgical and N95 Masks

Unlike other mask efficiency test, this one tested against a live test microorganism. The experiment followed ASTM testing guidelines, except that it replaced the standard test microorganism with a different one that more closely resembles the size of the SARS-CoV-2 (Covid-19) virus. The test setup looks like this:

Most fabrics had at last a 50% filtering efficiency, the cotton mask with a vacuum cleaner bag had 98.8% efficiency, and N95 and surgical masks scored over 99%.

Source Control

These experiments studied the effectiveness of masks under conditions that asses their use as source control.

Ability of fabric face mask materials to filter ultrafine particles at coughing velocity

This is another particle filtration efficiency test, but at high velocities to simulate coughing. As usual, all materials blocked some particles, with HEPA vacuum bags blocking more than even N95 masks. The best filtration was provided when combining fine cotton with non-woven materials.

Performance of fabrics for home-made masks against the spread of COVID-19 through droplets: A quantitative mechanistic study

This study examined the ability of various materials to absorb droplets. Droplets are bigger than aerosol particles, but they are also flexible enough to squeeze through pores in the filter. Researchers squirted mists of droplets at various fabrics and measured how much got through. (The experimental setup is surprisingly complicated and involves nanoparticles.)

Procedure masks did very well, as did polyester dish cloths and used silk shirts. Used cotton shirts, polyester bed sheets, and blended fabric did well also. Double or triple layers of even poor-performing fabrics also did well, and offered much better breathability than a procedure mask.

Wearing Masks

Masks are meant to be worn, which brings up issues of whether they fit the human face well enough to avoid letting in unfiltered air. These experiments attempted to study the effects of wearing masks on real and artificial heads.

Testing of Commercial Masks and Respirators and Cotton Mask Insert Materials using SARS-CoV-2 Virion-Sized Particulates: Comparison of Ideal Aerosol Filtration Efficiency versus Fitted Filtration Efficiency

This study used silica particles, and focused on the interplay between the filtering efficiency of the materials and the fit of the mask on a head-shaped object with air sampling ports. In a sealed test cartridge, the 600 thread count cotton fabric removed only 17.4% of small particles. Coffee filters and shop towels didn’t do much better. A Filtrete 1500 HVAC filter jumped up to 70%, KN-95 material and a 3M N95 mask all did very well. When fitted to a head-shaped form as a mask, however, all materials did poorly — between 15% and 40%. This was attributed to leaks around the nose and jawline.

Professional and home-made face masks reduce exposure to respiratory infections among the general population

This 2008 study compared 3 different masks worn by volunteers for a short 15-minute task. Particulate counts were taken inside and outside the mask. The teacloth masks filtered 55% to 69% of particulates, the surgical masks filtered 76% to 81%, and the FFP2 mask (European version of N95 mask) filtered 98% to 99%. A 3-hour experiment produced similar numbers, with teacloth masks filtering 58% to 70% of particulates, the surgical masks filtered 72% to 85%, and the FFP2 mask filtered about 99%. Tests with children varied a bit depending on the length of the experiment and the type of mask.

Effectiveness of Face Masks in Preventing Airborne Transmission of SARS-CoV-2

This experiment was done with live SARS-CoV-2 virus inside a test chamber inside a biosafety level 3 facility. The researchers constructed a physical simulation of airborne transmission of SARS-COV-2 in both droplet and aerosol form.

You really have to see the setup:

They used a nebulizer to create a mist of virus-containing droplets which were expelled out the mouth of a mannequin head. Another mannequin head was attached to a ventilator to simulate normal human breathing. Then they put masks on the heads and tested how the virus spread.

All masks were more effective when worn by the “spreader” mannequin than the “breathing” mannequin, but even when the “breathing” mannequin wore the masks, a well-fit N95 masks blocked 80% to 90% of the virus, surgical masks blocked about 50%, and even cotton masks blocked 20-40% of the virus. All masks therefore had at least some protective effect.

Real-World Studies

Having established that well-fitting masks of appropriate materials can filter exhaled infectious droplets and particles, and that they can protect the wearer from inhaling infectious droplets and particles, the next step is to see if any of these mechanisms work in the real world. All of these are observational studies.

Mitigation

This group of studies examine the effects of masking from the point of reducing infections in the population, but they don’t distinguish between source control and direct protection of the wearer.

Absence of Apparent Transmission of SARS-CoV-2 from Two Stylists After Exposure at a Hair Salon with a Universal Face Covering Policy – Springfield, Missouri, May 2020

“An investigation of a high-exposure event, in which 2 symptomatically ill hair stylists interacted for an average of 15 minutes with each of 139 clients during an 8-day period, found that none of the 67 clients who subsequently consented to an interview and testing developed infection. The stylists and all clients universally wore masks in the salon as required by local ordinance and company policy at the time.” [Summary from CDC.]

Reduction of secondary transmission of SARS-CoV-2 in households by face mask use, disinfection and social distancing: a cohort study in Beijing, China

“In a study of 124 Beijing households with laboratory-confirmed cases of SARS-CoV-2 infection, mask use by the index patient and family contacts before the index patient developed symptoms reduced secondary transmission within the households by 79%.” [Summary from CDC.]

In-flight Transmission of SARS-CoV-2: a review of the attack rates and available data on the efficacy of face masks

“Investigations involving infected passengers aboard flights longer than 10 hours strongly suggest that masking prevented in-flight transmissions, as demonstrated by the absence of infection developing in other passengers and crew in the 14 days following exposure.” [Summary from CDC.]

Association Between Universal Masking in a Health Care System and SARS-CoV-2 Positivity Among Health Care Workers

This is a study of 9850 workers in the Mass General Brigham healthcare system during a period in early 2020 in which the masking policy changed.to include universal masking of healthcare workers and then universal masking of patients. The study looked at the change in the slope of a weighted curve of test results to detect the effect, if any, of masking. Masking appears to have produced a decline in test positivity despite an increase in case numbers in the surrounding community.

Face Masks Considerably Reduce COVID-19 Cases in Germany: A Synthetic Control Method Approach

This study examined the effects of masking mandates in Germany, taking advantage of the fact that regions enacted mandates at different times to untangle some confounding factors. The study found that masking reduced the daily growth rate about 40%.

Trends in COVID-19 Incidence After Implementation of Mitigation Measures – Arizona, January 22-August 7, 2020

This report studied a combination of mitigation measures — including reducing the size and number of public events, reduced capacity in restaurants, curbside pickup, voluntarily movement limits, masking, and closing bars, gyms, and movie theaters — that appear to have suppressed the COVID-19 epidemic in Arizona.

Community Use Of Face Masks And COVID-19: Evidence From A Natural Experiment Of State Mandates In The US

This is similar to the German study, but using data from masking mandates enacted at different times in different locations in the U.S. The study found declining daily case rates of 2% over the three weeks following the mandate (similar to the German study).

Face Masks, Public Policies and Slowing the Spread of COVID-19: Evidence from Canada

This is the Canadian version of the U.S. and German studies, and it finds masks produced a 25% reduction in weekly growth.

Causal Impact of Masks, Policies, Behavior on Early Covid-19 Pandemic in the U.S.

This study from September examines a number of mitigations using policy data from the CUSP dataset as the independent variable and COVID data from the usual sources to study the effects of 6 mitigation methods: Stay-at-home orders, closed nonessential businesses, closed schools, closed restaurants, closed movie theaters, and face mask mandates for employees in public facing businesses. Because they have timing data for each type of mitigation in each state, they can statistically untangle the effects of the mitigation measures. The researchers estimated that face mask mandates for employees reduced the growth rate of infections by 9% to 15%.

Association of country-wide coronavirus mortality with demographics, testing, lockdowns, and public wearing of masks

This was similar in concept to the previous study, but for countries instead of states for the first 4 months of 2020. The researchers found that countries where people wore masks (either because of mandates or culture), Covid-19 mortality rates rose at 16% per week, compared to 62% per week for non-masking countries.

Face Masks and GDP

This is an analysis from June of 2020 by researchers at Goldman Sachs on the effectiveness of mask mandates at increasing community masking, the effectiveness of masks at reducing virus transmission, and the economic impact of using masking as an alternative to lockdowns. Using data from 20 states and D.C., they estimate that a nationwide mask mandate would increase mask usage by 15%, and produce a 25% reduction in infection growth rate. Replacing lockdown policies with a risk-equivalent masking policy would allow the country to reduce lockdowns by enough to allow GDP to increase by almost 5%.

Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: a systematic review and meta-analysis

Review and meta-analysis of 172 observational studies for the effects of social distancing and masking in healthcare and community settings found a large reduction of risk of infection if people wore masks.

Protection

A few observational studies focused on whether wearing masks protected the wearer.

Case-Control Study of Use of Personal Protective Measures and Risk for SARS-CoV 2 Infection, Thailand

“A retrospective case-control study from Thailand documented that, among more than 1,000 persons interviewed as part of contact tracing investigations, those who reported having always worn a mask during high-risk exposures experienced a greater than 70% reduced risk of acquiring infection compared with persons who did not wear masks under these circumstances.” [Summary from CDC.]

SARS-CoV-2 Infections and Serologic Responses from a Sample of U.S. Navy Service Members – USS Theodore Roosevelt, April 2020

“A study of an outbreak aboard the USS Theodore Roosevelt, an environment notable for congregate living quarters and close working environments, found that use of face coverings on-board was associated with a 70% reduced risk.” [Summary from CDC.]

Randomized Trials

All of the real-world studies I mentioned so far were observational studies, which look at differences in the real world and try to explain them. One of these weaknesses of these studies is the problem of confounding variables. That is, sometimes you think you’ve detected an effect based on the variable you’re studying, but the effect is actually based on a different variable that has some relation ship to what you’re studying.

If you know what some of the confounding variable are, you can use statistical procedures to untangle the effects of the different mitigations, including the one you want to study. When you do this, you are said to be controlling for the other variables. The problem is that this won’t work for variables you can’t get data for. And it seriously won’t work for variables you haven’t even thought of.

A better way to control for confounding variables is to use a randomized trial: You randomly choose some people to receive the mitigation and others to be in the “control” group. Because your selections are random, they won’t be correlated to any of the natural confounding variables (including variables you haven’t even thought of) so there is less chance of misidentifying the cause of observed effects. Even if there are variables you haven’t controlled for, they will be “randomized away.”

This switch from passive observation to active intervention can raise ethical issues. For example, you probably wouldn’t get IRB approval for an experiment in which you randomly instruct a control group of people to go unmasked in the middle of a deadly pandemic. This limits the methodology of possible experiments.

Face mask use and control of respiratory virus transmission in households

This was a 2009 study conducted with 143 households in Australia in which a child member of the household had a respiratory infection such as the flu or a cold. The households were randomly assigned to three groups:

• 47 received P2 respirators (similar to N95) to be worn at all times around the sick child.
• 46 received surgical masks to be worn at all times around the sick child.
• 50 were in the control group and received nothing.

And as it turns out, at least half the participants with masks decided not to wear them. But for those who did, the daily risk of becoming infected was reduced by 60% to 80% .

There’s one other randomized trial…

The Danish Study

Yes, I’m finally ready to talk about the Danish study, which is this:

Effectiveness of Adding a Mask Recommendation to Other Public Health Measures to Prevent SARS-CoV-2 Infection in Danish Mask Wearers

This is a randomized trial designed to determine if the observed effectiveness of community masking in the Covid-19 epidemic is due to source control effects or personal protection effects. In other words, does wearing a mask protect you?

In order to avoid the ethical danger zone of telling someone not to wear a mask, this experiment recruited 6000 people who already did not wear masks while working outside the home for at least 3 hours per day (which was common at the time). They were randomly divided into two groups: The mask group and the control group. Both groups were encouraged to use social distancing, but the mask group was given additional instructions to wear masks when outside the home and given 50 disposable procedure masks and instructions on how to use them. (This approach was likely chosen to meet ethics requirements by ensuring that neither group was made worse off by participation in the experiment.)

Results

The experiment ended after 30 days with a fairly weak result. The study found that masks produced an 18% reduction in infections, but with a significance of p=0.33, meaning that even if masking did nothing, there’s still a 1 in 3 chance this experiment would have shown an 18% effect. That’s so high as to be meaningless. As a rule of thumb, we generally want p to be less than 0.05. But the most that the Danish study can say with a significance of p=0.05 is that the effect of masking falls somewhere between a 46% decrease in infections and a 23% increase in infections, which is not very useful.

You many have noticed that, as described, the experiment did not technically study the effects of wearing masks. Rather, it studied the effects of telling someone to wear a mask and giving them free masks, which is not the same thing. If some of the people in the mask group didn’t wear masks, it would dilute the ability of the experiment to measure the true effect of wearing masks, so they might be more effective than they appeared.

Basically, this experiment neither proved that masks will protect the wearer nor ruled it out. The experiment lacked the power to answer the question.

Conclusion

The Danish study was conducted in a time and place where few people wore masks, meaning that almost no source control was possible. Thus this study does not in any way invalidate the concept of wearing masks to protect others, which has always been a key motivation in Covid-19 community masking efforts.

In fact, the real-world observational studies I listed above all found that community masking led to a meaningful reduction of infections. This seems like a pretty firm basis for concluding that community masking helps reduce the spread of Covid-19.

As for whether wearing a mask will protect you, as I said in my original post about the types of masks, the evidence there is not as strong. There’s certainly a lot of evidence that it ought to work. Multiple studies show that a variety of masking materials are capable of filtering droplets and/or aerosols with properties similar to those that carry Covid-19 virions (one study even showed this with actual live SARS-CoV-2 virus). Several studies also show that masks can be fit to a human face well enough to filter inhaled air, which should provide protection.

In addition, we have three studies that show a protective effect in the real world:

• The Australian at-home masking experiment for colds and flu, which found a 60% to 80% protective effect.
• The Thai contact tracing analysis, which found a 70% protective effect.
• The USS Theodore Roosevelt investigation, which also found a 70% protective effect.

The Danish study, on the other hand, doesn’t show a protective effect. In fact, it can be interpreted as capping the size of the protective effect — at least for the environment in which the experiment was conducted — because if procedure masks offered much better than 50% protection, the study should have picked it up. Scientists have ideas, but no compelling answers, as to why this study differs from the others.

As for my own opinions about masking, I stand by my earlier statements. There’s some reason to believe that wearing a mask may protect you from Covid-19. That seems even more likely if the mask is a filtering facepiece respirator, such as an N95 or KN-95 mask, which was was designed to protect the wearer from this kind of threat. Frontline healthcare workers all over the world have been using these masks for months, and while I’m not aware of any studies on the masks’ efficacy against Covid-19 in real-world healthcare settings, healthcare workers seem to think they’re worth the trouble.

For all these reasons, filtering facepiece respirators were a large part of my mask posts, and I still think they should be effective, and it’s likely that procedure masks and even cloth masks provide some protection.

This post by Mark Draughn at Windypundit was originally published at The Danish mask study and the evidence for community masking

As I said before, I’m doing this with some trepidation because I’m not entirely sure this is the right thing to do. That’s because, to be very clear, I am not an expert in this field. I’ve seriously considered not posting anything at all for fear giving out bad information. But the thing is…I think I know some stuff that might actually help people.

So, now that I’ve fulfilled my duty of explaining my level of knowledge (not a lot, but more than some) and warning you that I might not know what I’m talking about, even though I think I do, let me see if I can offer you some advice about masks.

Mask Use and Care

I occasionally shoot some guns — paper targets and plinking, mostly — so I’ve had firearms safety training, and I’ve learned the basic rules about keeping my finger off the trigger and never pointing the gun in an unsafe direction. Another of the safety rules is “Always treat every gun as if it were loaded.” That means that even if you’ve unloaded the gun, you don’t go waving it around and pointing it at people. You always handle it safely.

I try to take a similar approach to wearing a mask (and other infection control matters, such as hand sanitization). I just always wear one if I’m likely to run into other people. Always is a simple rule to remember.

And yes, I do wear the mask over all my face holes, like you are supposed to.

When wearing ear loop masks — procedure or KN-95 — I’ve found it difficult to get a good fit without hooking the ear loops on some kind of mask extender. That allows me to move the mask extender up and down and adjust how far back the ear loops attach, so I can get a snug fit across my face.

Personally, I find cloth masks easy to breath through, and procedure masks aren’t much worse, but when I move up the protection scale to N-95 filtering facepieces, I find that breathing gets harder.

There is some evidence that respirators will cause you to re-breath a little extra little carbon dioxide, but the result is no different from what happens if you exercise, causing your body to produce more carbon dioxide. In either case, the solution to rising carbon dioxide is to take slightly deeper or more frequent breaths to increase the rate of gas exchange in your lungs. You’ll do this automatically, as you do when exercising, but you might find it more comfortable to transition if you force yourself to breath a little heavier, until you get used to the mask.

Another problem I noticed when wearing a respirator is that it functions a bit like a scarf, trapping warmth near my face, which make the air coming in a little warmer. Over the summer, this would get uncomfortable if I exerted myself. I suspect that people with medical conditions such as COPD would need to be careful wearing a respirator.

Mask Reuse

Cloth masks and respirators with replaceable filters are supposed to be reused, but all of the disposable masks I’ve described were intended to be used once and discarded. Given the shortage, however, even frontline medical personnel have to reuse masks for days, and you’ll probably want to do so as well, unless you are using cheap procedure masks, and even then you’ll probably want to keep the mask all day.

The CDC has approved reusing N-95 masks 5 times, but that’s under healthcare conditions. You can probably get away with more, but keep in mind that particle filtering masks do get clogged with particles and eventually you’ll need to switch to a new mask.

But in the meantime, you can use the ones you’ve got over and over…

Donning and Doffing

Since a used mask might be contaminated with Covid-19 virions, you should handle it carefully so as not to contaminate yourself. Here’s a nurse explaining the careful procedures for doing this in a healthcare environment:

There are quite a few of these videos on YouTube, and from watching several of them, the key points seem to be:

• You should assume the outside of the mask is contaminated, and you should be careful not to handle the mask in a way that would transfer the exterior contamination to
  • the inside of the mask or
  • your face.
• In other words, if you have to touch the outside of the mask, don’t touch the inside of the mask or your face until you’ve sanitized your hands again.
• Whether putting on the mask or taking it off, sanitize your hands twice: Once before handling the mask, and again after you are done handling the mask. (I keep a small refillable bottle with me whenever I’m out for just that purpose.)
• Note that the nurse is using gloves. As she points out, she removes them incorrectly to save them. The correct procedure is a glove-in-glove technique.

Don’t worry if you don’t get it right every time. Unlike these nurses, you’re not working a Covid ward, so you have a lot more leeway to make mistakes. Just try to get it right as often as you can.

Masks can wear out in a variety of ways which you should watch out for. Try to notice if breathing is getting more difficult, and inspect the mask for worn or soiled filters. Don’t forget to inspect the straps, which can wear out or be damaged by use.

Sanitizing Masks

Reusable masks — both cloth masks and reusable respirators — are made of all kinds of different materials, some of which require delicate soap-and-water cleaning, some of which you can toss in the washing machine, and some of which you can put in boiling water in a microwave. Regardless of whether it’s a simple source control mask or an actual respirator, you have to read the manufacturer’s instructions to sanitize it the right way without damaging it.

Disposable masks, on the other hand, were never meant to be reused, so there won’t be any cleaning instructions from the manufacturer. The users of the masks, including healthcare workers, have been trying to figure out the best way to sanitize them. I’d like to tell you what works, but I’ve seen some contradictory information, and I’m not sure what works best. The CDC seems to be very suspicious of the whole idea, and while they have approved some decontamination devices, they don’t endorse a do-it-yourself process.

Nevertheless, people are doing it. The basic approach seems to be some combination of heat and time. During the summer, I used to just leave masks in the car on a sunny day, when the interior got up to about 130°F (yes, I measured it). I don’t know how long it takes to kill the Covid-19 virus, but the FDA pasteurization tables say food is safe after 2 hours at that temperature, so I figure a couple of days should make extra sure.

Now that it’s cooler, I just leave masks sitting somewhere for a week or so and let time and air destroy the virus. (I briefly thought of leaving masks hanging over a heating register where the warm dry air would sterilize them more quickly, but came to my senses and realized this could blow Covid all over the room.)

Recently, I’ve seen explanations of how to use mild heat to sanitize disposable masks in electric cookers. Here’s a video explaining a process developed by scientists at the University of Illinois at Urbana-Champaign:

That sounds plausible, and they’ve got a paper out describing the process, but they make it clear they offer no guarantees, and they have no idea how much you can safely deviate from this process. A different cooker, for example, might overheat and damage the masks, or it might detect the overheating condition and shut down before decontamination is complete.

Also, unlike these scientists, you and I have no way to measure how effective the decontamination process was, and no way to test the filtration efficiency of the masks to make sure they haven’t been damaged. If you try something like this, and I’m not saying you should, keep the temperature under control and inspect the masks for damages.

If you look around, you can find other videos showing other ways to decontaminate masks. The do-it-yourself community hasn’t yet settled on a way that is effective and difficult to screw up.

Meanwhile, I have heard of a few things you probably should not do when cleaning a mask:

• Don’t use a high temperature process because that could melt the mask or the straps.
• Don’t put the mask in the microwave. The metal parts used to shape the mask could be damaged and start a fire.
• Don’t use chemicals like chlorine, alcohol, or hydrogen peroxide. Some of them are dangerous to handle, especially if heated, and they could damage the properties of the filter that allow it to collect small particles. Also, you don’t want to be inhaling some of those fumes when you wear the mask all day.

And now, one final topic…

What’s the Ultimate Respirator?

I was going to put this in the buyer’s guide section, but it was getting too long, and this is not really a serious option, but I wanted to figure out the ultimate price-is-no-object respirator that would give you the most possible protection.

Realistically, it’s probably just a hard-to-get medical grade N95 filtering facepiece respirator, or maybe a half-mask with appropriate cartridges and a filter for the exhalation vent.

But unrealistically, there are a couple of fun options:

In theory, this kind of firefighter-style Self-Contained Breathing Apparatus (SCBA) setup with a tank of air on your back would do the trick nicely, but it’s really impractical and you have to replace the tank every 60 minutes so you need to carry around a lot of spare tanks if you’re going to be out for a while.

If you’d rather carry around batteries than air tanks, you can get a Powered Air Purifying Respirator (PAPR):

PAPR systems use a full hood over your face that is fed filtered air from a battery-powered blower that you can hang around your waist. The blower creates positive pressure in the hood so that all air movement is from inside the hood to outside, preventing any droplets or aerosols from traveling the other way and infecting you.

Even with a loose fitting hood (pictured above) you get at least twice the protection of an N95 mask and you can keep your facial hair. With a tight-fitting hood, PAPR systems are extremely effective — some are rated to provide 100 times the protection of an N95 mask.

Sadly, both the PAPR systems and SCBA come with a number of downsides:

• They are expensive. PAPR systems cost between $1000 and $3000 and SCBA systems cost between $2000 and $4000. (I have no idea what you get for the higher prices.)
• These are complex pieces of machinery that require training and maintenance and refilling of tanks or recharging of batteries.
• Both systems spew waste air out into the environment, making them almost the opposite of source control. If you have Covid, these will make sure everybody around you gets it.

This post by Mark Draughn at Windypundit was originally published at Windy’s Guide to Masks – Part 4: Mask Use and Care

As I said before, I am not an expert in this field. I’ve seriously considered not posting anything at all for fear giving out bad information. But the thing is…I think I know some stuff that might actually help people.

So, now that I’ve fulfilled my duty of explaining my level of knowledge (not a lot, but more than some) and warning you that I might not know what I’m talking about, even though I think I do, let me see if I can explain the different types of masks you are likely to encounter.

Cloth Masks

They tell you any sort of mask will help, and it’s probably true, but masks made of ordinary cloth such as the cotton weave used to make T-shirts are not particularly good at filtering small particles: If you can see the holes in the weave, microscopic virus particles can easily make it through. Nevertheless, as long as the mask absorbs some of the the droplets you exhale, it will provide some degree of source control.

Experts generally recommend that one of the inner layers should be a “non-woven” material. In theory, that’s any cloth or fabric material where the strands that make it up are held together by more than just a mechanical weaving process. There are a variety of such materials, using various glues and bonding techniques, but in practice when discussing respiratory masks, this means a “melt-blown” material. That’s a process where melted microscopic strands of material are blown together so they form a layer of porous material that acts as a filter.

There’s another type of mask that uses non-woven materials…

Procedure Masks

Those are the kind of mask you think of when you normally think of a doctor or nurse wearing a mask. You know, one of these things:

Procedure masks should have at least three layers: Inner and outer moisture absorbing layers, and a middle layer made up of melt-blown filtering material. These are designed for use in medical procedures, to protect patients from respiratory diseases carried by the person performing the procedure. That is, they are for source control, which is how we protect each other.

What these procedure masks are not designed to do, however, is protect the wearer from disease-carrying droplets from other people. Wearing one of these masks is not intended to protect you at all.

But…

Secrets of the Procedure Mask

Despite what I just said, procedure masks will protect you…some. Probably.

[When I first started drafting these posts, I was going to use a clickbait title about “mask secrets” or something like that, because some of this stuff was believed true by many experts but not yet acknowledge by public health authorities. Time has caught up with me, but a few sections, like this one, are still in that format.]

Make no mistake, the primary benefit of such masks is protecting other people from Covid-19-containing droplets that you might be exhaling. However, if you inhale through one of these masks, the melt-blown filter material should snare some of the Covid-19 droplets out of the air, and potentially even some of the Covid-19 aerosol particles. Not all of them, and maybe not even most of them, but certainly some of them. And like I said, protection from infection is a numbers game.

That’s one of the secrets of the mask business during a pandemic: Just because a mask wasn’t designed to protect you, and just because they have not been FDA approved to protect you, doesn’t mean they won’t in fact protect you.

Really? Has that been scienced?

Until recently, there has not been a lot of scientific study in this area. Some scientists testing masks for protection against air pollution found that the surgical masks they tried filtered out about 80% of particulate pollution. By comparison, the medical standard N95 mask filters at least 95% of particulate pollution. On the other hand, a cotton handkerchief filtered out only 28% of pollution. They were testing against simulated automotive exhaust, and there’s more than one type of surgical mask, so…the applicability of this study to our current pandemic is a bit weak.

There was a more real-world study in which 2,862 healthcare personnel were randomly assigned to wear either surgical masks or N95 masks, while caring for patients with the flu, and the nurses wearing surgical masks did not catch the flu significantly more often than those wearing medical N95 masks. Another similar study found similar results, as did a study of ordinary citizens caring for flu-stricken children at home.

There are lots of issues you could raise with these studies, and none of this is comparable to the situation we find ourselves in with Covid-19, but it has for some time seemed likely to me and others that surgical masks do offer some level of protection to the wearer.

And there may be something to that: The CDC recently announced results from a group of studies indicating that wearing a mask seems to protect you from Covid-19 by reducing your chances of inhaling droplets. The study doesn’t mention aerosols, and the experiences of healthcare workers caring for Covid patients without proper protective gear strongly suggests that surgical masks are not a complete substitute for standard N95 masks.

I’ll get to those N95 masks, but first we need to talk about…

Respirators

You’ve undoubtedly heard about the use of N95 masks by healthcare workers. N95 masks may look similar to procedure masks or one of the other masks you see people wearing, but they are radically different, because they aren’t just masks, they are respirators. The key difference is that unlike a procedure mask, which may filter the air you breath but wasn’t designed with that in mind, a respirator is in fact designed to provide you with safe air to breath.

Respirators come in a variety of types. In the most extreme situations, the respirator comes with a supply of safe air. When a firefighter enters a burning building where the air is filled with dangerous fumes and might not have enough oxygen, they wear a fully self-contained breath apparatus (SCBA) which includes a tank full of breathable air.

In less extreme situations, it is sufficient to provide the wearer with ambient air that has been filtered to remove the expected contaminants. In many industrial applications, workers wear reusable half-face respirators that cover the mouth and nose. These masks filter inhaled air through replaceable cartridges, such as those on either side of this mask:

The particulate filtration standards for respirators are set under public health regulations in 42 CFR 84, administered by the National Institute for Occupational Safety and Health (NIOSH), a division of the Centers for Disease Control (CDC). NIOSH particulate standard designations consist of a letter and a number. The letters will be one of N, R, or P, which specify increasing resistance to degradation of the particulate filter due to oil vapors (an important issue for industrial users). The number is either 95, 99, or 100, indicating that the filter removes 95%, 99%, or 99.97% of particles, respectively. An N95 filter therefore removes 95% of particulates but should not be used where oil vapor is present.

(The mask above appears to be a 3M mask with multi-gas filtration cartridges. The white outer parts of the cartridges are filter retainers that probably contain N95 or P95 particulate filters.)

In a medical environment, such complex filtering systems are unnecessary and even counterproductive. Hazardous chemicals are not a concern, so gas-filtering cartridges are unnecessary. The biggest threat is biological contagions such as bacteria and viruses, which are essentially particles that can be removed by particulate filtration alone, and resistance to oil is not required.

Furthermore, healthcare personnel are concerned about cross-contamination between patients — e.g. accidentally transferring viral particles from a Norovirus patient in one room to an influenza patient in another — so they prefer to replace protective gear between visits to patients, which can be an unwieldy process with complex reusable respirators, which would have to be sanitized. That’s why healthcare workers prefer disposable respirators.

N95 Masks

That brings us to what’s known as a filtering facepiece respirator, which is what most people mean when they talk about an “N95 mask.” It’s basically a piece of N95-rated particulate filtering material that is shaped to fit over your mouth and nose to filter disease-causing particles from the air you inhale. And you can throw the whole thing away when you’re done with it and ready to move to the next patient.

(Or you could back in the pre-Covid-19 days when they only cost 75 cents and every hospital had storage rooms full of them. Nowadays, healthcare workers follow careful procedures to safely reuse the same mask for hours or days.)

Unlike a procedure mask, which is flat, an N95 mask has a 3-dimensional cup or pouch shape that allows it to bulge out over your nose and lips while keeping the edges in contact with your face. In addition, instead of loops over the ears, the mask is held in place by tight straps that go around your head and neck to hold the mask firmly pressed against your skin. They are uncomfortable to wear for long periods of time, and healthcare workers who take care of Covid patients often develop skin irritation.

In addition to complying with the NIOSH N95 standard, these filtering facepiece respirators have to be approved by the FDA when used for medical purposes.

But wait…

You may be wondering, if N95 masks are so great, how come they didn’t do any better than procedure masks in the studies I mentioned above? After all, they filtered more of the test particles than procedure masks. Shouldn’t they have performed better in the real-world studies?

The truth is, no one knows why those studies turned out the way they did. The question didn’t seem important enough at the time to do more studies. All we can do is speculate. N95 masks are less comfortable than surgical masks, so maybe study subjects were less compliant about wearing them. Another possibility is that influenza is more likely to be spread by people contaminating their hands and touching their faces, and both masks discourage face touching equally.

There’s at least one more important possibility…

Fit

If the filtering material in a procedure mask is good enough to stop a virus — or at least most of the virus — why are they only partially effective at protecting the wearer? Why do some people with N95 masks still get Covid?

One answer is fit. In order for an N95 respirator to clean the air you breath, all of the air has to flow through the filtration material. But the filtration material slows down air flow considerably, so if there’s even a small gap around the edge of the mask, a lot of outside air will flow through the gap instead of passing through the filter, which makes the N95 respirator no more effective than a procedure mask.

This is why medical personnel who wear N95 masks have to undergo special training and periodic fit testing using special equipment, to ensure they can wear an N95 mask correctly. There is usually also a fit-checking step that healthcare workers are expected to follow every single time they put on an N95 mask to make sure that mask is fitting correctly. The whole fit testing process varies from one mask model to another, but just as an example, here’s a short video on how to don the 3M model 1860 mask, including how to do a fit check:

(Fit check instructions vary between manufactures and mask models. If you buy N95 masks, read the instructions.)

Because of these complexities, many health authorities recommended against ordinary people using N95 masks because they wouldn’t be able to wear them correctly.

Secrets of the N95 Mask

That leads me to another one of those mask secrets: If you can get N95 masks, it’s OK for you to wear them. First of all, if you fit the mask incorrectly, and the seal against your face is leaky, your mask won’t be any worse than a procedure mask, which has no seal at all. Second, you’re not a healthcare worker in a Covid ward. They spend all day working with people who are very definitely shedding the Covid-19 virus in their breath, so even a minor breach in their defenses can lead to infection. You face much less of a threat, so you don’t need to be perfect. As I said, it’s a numbers game, and a slightly leaky N95 mask is still going to be an advantage.

(Anecdotally, I’ve worn industrial-grade N95 masks when doing woodworking, especially when sanding, and despite the fact that I received no training or fit testing, they made a big difference in my level of comfort, which implies that much of the air was filtered.)

Is N95 Good Enough?

On the other hand, maybe you wonder if 95% filtration is good enough. And if you ever read the technical specifications for the NIOSH N95 test, you may have noticed it uses particles that are 0.3 microns in size, whereas SARS-CoV-2 virions are considerably smaller — somewhere between 0.2 and 0.05 microns, according to Wikipedia. Won’t they just slip right through?

Basically, N95 is good enough for two reasons:

First of all, particulate filters do not work like a sieve. Or at least, not just like a sieve. Larger particles are indeed trapped because they cannot fit between the fibers of the filter, but smaller particles are trapped by a variety of other mechanisms, such as sticking to a fiber through electrostatic charge. The physics of particle filtration are non-intuitive and complicated, and I’d be lying if I said I understood them, but think of it this way: To a virus particle 0.1 microns in size, a piece of filtration material a millimeter thick is a forest of fibers 10,000 times its size. That’s a long way to go without getting stuck to something. (The New York Times has a pretty decent illustrated explanation of how filtration works.)

In practice, there’s a gap between the sieve mechanism that catches the larger particles and the other mechanisms that catch the smaller particles, and that gap occurs with particles around 0.3 microns in size. That’s why NIOSH tests are done with 0.3 micron particles: To measure the masks at their worst. This means that since SARS-CoV-2 virions are smaller than 0.3 microns, they are actually captured more efficiently than the 95% capture rate for 0.3 micron particles.

The second reason N95 is good enough is that the 95% filtration rate is a minimum standard, so manufacturers tend to aim for a higher average filtration rate to minimize the number of masks that are rejected by the testing process due to manufacturing variations.

If you’re wondering whether N99 or N100 masks would be better, I can’t really say. But medical professionals seem happy with N95 masks, and the rate of infection among healthcare workers isn’t much higher than the general population, despite the exposure to Covid patients.

Next: Part 3: Buying Guide

This post by Mark Draughn at Windypundit was originally published at Windy’s Guide to Masks – Part 2: Types of Masks

That’s because, to be very clear, I am not an expert in this field.

What I am is curious about the technology involved, and I’ve therefore spent a bit of time trying to learn the basics of how masks protect us. My wife refers to me as a “PPE Enthusiast,” and I think that’s a pretty accurate characterization of my level of knowledge. And if I was talking about cameras or programming languages or something like that, I wouldn’t hesitate to give you my opinion.

But this is a matter of life and death, so I feel some caution is warranted, and I’ve seriously considered not posting anything at all for fear giving out bad information. But the thing is…I think I know some stuff that might actually help people.

So, now that I’ve fulfilled my duty of explaining my level of knowledge (not a lot, but more than some) and warning you that I might not know what I’m talking about, even though I think I do, let me see if I can offer you some advice about masks, starting with some basics about how we spread Covid-19.

Note about terminology: COVID-19 is a respiratory disease that is caused by a new strain of coronavirus called SARS-CoV-2. To keep things simple, I’ll just be calling everything “Covid-19” or just “Covid” here.

Source Control

Most of the public health discussion about masks for Covid-19 is about what’s usually referred to as source control — preventing infections from spreading by stopping them at the source. For a respiratory infection, that means covering the breathing holes in your face with some kind of filter that catches the germs when you cough, sneeze, sing, talk, or even just exhale.

Germs are really tiny things — a human hair is about 500-700 times thicker than a single Covid-19 virus particle — but fortunately exhaled virions don’t usually travel alone. They’re usually stuck in all kinds of gooey fluids, and the resulting droplets of goop can be rather large, often large enough to see with the naked eye, especially when lit correctly, as in this photo of a sneeze:

That mess is what a source control mask is all about. If those droplets contained the Covid-19 virus, and someone inhaled one of them, there’s a pretty good chance they’d become infected.

Fortunately, it doesn’t take much to stop those big droplets. In everyday pre-pandemic life, people would cover their mouths with a handkerchief or paper towel when they sneezed or coughed. (And you may remember that very early in the pandemic they were advising people to sneeze into the crook of their elbow, just to absorb some of the mess.) What that implies is that you can achieve some measure of source control for Covid-19 with even a low quality mask, because it’s the equivalent of having a handkerchief positioned over your mouth and nose at all times, ready to catch any droplets you might exhale.

(It’s relatively easy to prove in a lab that masks will block exhaled particulates from talking or coughing. But studying the effectiveness of community masking — determining if mask wearing by large groups of ordinary people will actually prevent the spread of respiratory diseases — is harder. Prior to Covid-19, the studies were few and the results were mixed. But now that everyone in the world is part of a natural experiment, a whole bunch of studies seem to offer good evidence that masks are effective.)

If this were some other disease, we might just wear masks when we were sick, but with Covid-19, we unfortunately can never know when we might exhale droplets containing the Covid-19 virus…

Symptomless Spreaders

One of the shocking early lessons of the Covid-19 pandemic was that people can spread the disease even if they’re not sneezing and coughing or, in fact, showing any other symptoms. Unlike many other respiratory diseases, the ordinary exhaled breath of someone showing no symptoms can still carry enough virus particles to infect someone nearby. Consequently, you can catch Covid-19 and then spread it to other people before you know you have it.

There was a somewhat confusing announcement from some World Health Organization scientists claiming that “asymptomatic” people did not spread Covid-19. Those scientists were using a highly technical definition of asymptomatic that refers only to infected people who never show any symptoms through the entire course of the disease, and even then it wasn’t entirely clear. But someone who shows any Covid-like symptoms, even symptoms so minor they don’t go to the doctor — or even realize it’s a symptom — could have infected other people before the first symptom occurred.

So just because you have no symptoms doesn’t mean that you aren’t infected. You could have it and not know it, and because you can infect other people with Covid-19 before you even know you have it, health authorities are recommending that we all wear masks at all times when we’re around other people.

That makes it sound simple, but I think it’s fair to say that there’s a non-trivial psychological burden: We have to behave at all times as if we are infected with a serious and potentially fatal disease. It takes a bit of getting used to.

Airborne

The sneezing man above illustrates how someone with Covid-19 can literally spread it through the air. As you can see in the picture, however, many of the largest droplets are already falling toward the floor, and most of the rest will settle out of the air within a few seconds. Now a sneeze like that can carry pretty far in a few seconds, but the droplets that come out of your nose and mouth when talking or breathing normally aren’t moving nearly as fast, so they don’t get very far before settling out. This is the intuition behind one of the reasons social distancing works, even without masks.

(The 6-ft rule, I should add, is just a rough guideline. Coming to within 3 feet, or even 1 foot, of a person with Covid doesn’t guarantee you’ll get it, and being 15 feet away doesn’t guarantee your safety. But further away is always better.)

One important complication is that not everything that floats in air is going to settle out. The three major gases that make up the Earth’s atmosphere — nitrogen, oxygen, and argon — have different densities, but they have not settled out in billions of years.

Somewhere in between droplets (which settle out in seconds) and gases (which never settle out) lies a middle ground made up of…

Aerosols

Aerosols are particles or droplets that are so tiny they don’t fall out of the air right away — they are continuously buffeted about by the natural movements of the air. Familiar examples are fog, the fine smoke from a cigarette, or the lingering smell after cooking a meal. These can stay in the air for many minutes or several hours, until they disperse or stick to something or eventually hit the ground..

In the early days of the pandemic, it was thought that under normal conditions, Covid-19 was only exhaled in droplet form, so aerosolized spread was not much of a risk outside of hospital settings (where certain procedures could aerosolize Covid-19 droplets). This was one of the reasons mask wearing was not encouraged in the early days of the epidemic — it’s not necessary if you’re keeping outside of droplet range.

Unfortunately, there has been mounting evidence for months, as the CDC has recently acknowledged, that people are exhaling Covid-19 particles in aerosolized form in quantities large enough to spread the disease. It is still not thought to be the most likely mechanism of Covid-19 spread, but since so many of us are mitigating against droplet spread by washing our hands, keeping our distance, and wearing cloth masks, aerosolized spread has become relatively more important.

Speaking of “relatively”…

The Numbers Game

Short of total isolation from the rest of humanity, you can’t make yourself perfectly safe from Covid-19. But you can control your level of risk, including the risk of aerosolized exposure. It’s a numbers game.

First of all, at least one viral particle — a virion — has to make it into your body and find a suitable host cell to successfully infect. No Covid-19 virions, no Covid-19 disease. Your body has some general-purpose defenses against viral infection, so the virion has to get a bit lucky to find a suitable cell to infect. Furthermore, scientists believe it generally takes more than one virion to cause the disease. I don’t understand why, and I’m not sure virologists have figured it out either, but in general, the more viral particles that make it into your body, the more likely you are to become infected, and (maybe) the more severe the disease is likely to be.

This means that the measures you take to mitigate the virus do not have to be perfect. Even a moderate amount of protection will improve your chances of avoiding infection, and if you get infected it might improve your chances of having a mild case. That is especially true when you pile on a bunch of different protective measures to reduce the risk of infection: They form a gauntlet that Covid-19 has to get through to get to you.

Here are some of the things you can control to reduce your risk:

• You can only catch Covid-19 from people who have it, so
  • avoid people who seem likely to have it, and
  • the fewer people you meet, the less likely you are to meet someone who has it, so avoid people in general and large groups of people in particular.
• Infected people breath out Covid-19, so the less they breath, the less Covid-19 you will be exposed to. Avoid people who are exercising, yelling, or singing. Silent people sitting quietly are your safest company.
• Even aerosolized Covid-19 disperses with distance, so the farther away you are from people who might be infected, the lower the level or your exposure. Distancing still helps.
• Speaking of distancing, the worst case of not distancing is getting Covid-19 virions on your hands and then touching your face. Wash your hands often, especially after touching other people or things other people have touched.
• Air flow disperses the virus as well, so outdoors is better than indoors, and good indoor ventilation is better than a stuffy room. (On the other hand, the wrong type of ventilation can just blow Covid-19 all over the room — imagine a Covid carrier sneezing in front of a fan.)
• When other people wear masks, they are less likely to spread Covid virions, so avoid people who are not wearing masks.
• Not only does your mask protect others, but it might help you as well, which is what the rest of this series of posts is all about.

None of these steps will make you completely safe, but you can, by combining these and other safety measures, make yourself considerably safer from Covid-19. Masks are part of that.

Next: Part 2: Types of Masks

This post by Mark Draughn at Windypundit was originally published at Windy’s Guide to Masks – Part 1: Basics

In general, he’s talking about charts of confirmed U.S. Covid-19 case counts per day, like this one that I posted on Friday:

First of all, the part about the second peak not being a second wave seems reasonable. I think it’s more accurate to describe that second peak as the the first wave sweeping over new population centers. When you break the U.S. down into smaller regions, there to appear to be single high peaks occurring at different times in different locations. On the other hand, I’m less convinced this is seasonal, rather than a simple matter of transmission dynamics: Transmission between metropolitan areas is somewhat bottlenecked compared to transmission within metropolitan areas, so spread from initially hard-hit metropolitan areas to new metropolitan areas takes time, but once it reaches a new metropolitan area, it explodes. But that’s just a theory.

El gato malo’s main argument appears further back in the thread, and he has some theories too.

The issue I have with el gato malo’s chart here is that by showing the line adjusting for testing level, he’s no longer just presenting data. He’s presenting a model. That’s not an unreasonable thing for someone to do when commenting on Covid-19 issues, but I think it would be a bad idea for the news media to invent their own model and report it as news, as el gato malo suggests. That, not reporting the raw numerical facts, would be “tantamount to lying.”

I disagree. Health agencies should not be reporting model outputs unless those models are well-established. Otherwise they should stick to publishing raw data, as should most journalism sources. Those of us who want to look at models can find (or build) them for ourselves.

The use of models is especially concerning because there’s usually more than one model for anything, and it’s entirely possible that a particular model promoted by a news outlet is wrong. Heck, they could all be wrong. As el gato malo’s model is.

The cat doesn’t include an explicit formula, but from what he wrote, his model for the true rate of infection appears to assume that for any given number of cases in a population at a point in time, the number of cases detected will be proportional to the number of tests run. He refers to the number of tests as the “sample rate” and mocks epidemiologists for not understanding sample rates:

The thing is, “any first year stats student” would be dinged on an exam for this mistake. Let me explain what El Gato Malo is thinking by describing an example where he would be right:

Suppose you’re a veterinarian at a national park and you want to know how badly the deer in the park are being hit by some deer disease — call it Bambi Syndrome 19. So you go out and take blood samples from 20 deer at random, and you find that 6 of them test positive for BS-19. Now that you know the disease is affecting the park’s deer population, your staff gets funding to do a larger survey to get a better picture, this time taking samples from 200 deer. You discover that 48 of them test positive for BS-19. Do you start panicking because eight times as many deer tested positive in the second survey as in the first?

Of course not. The second survey included 10 times as many specimens, so you’d expect a proportionate increase in positive results. The fact that the first survey had a 30% positive test rate, and the second only had 24% positivity is actually a good sign, because the problem probably isn’t as bad as the first survey indicated. In other words, when doing random samples, we should look at percentages (or ratios) of positive tests, not the absolute number of positive tests.

This is how el Gato Malo thinks we should treat Covid-19 testing. But this kind of thinking only works for random samples. A long as you’re taking random samples of a population, it’s safe to assume that, all other things being equal, the number of positive test results will be proportional. But Covid-19 testing in the United States doesn’t use random sampling. It doesn’t even come close.

Going back to my national park example, it’s as if the rangers brought in 10 sick deer (I have no idea if animal care at national parks really works this way, but go with it) and you diagnosed 9 of them with BS-19. (The 10th one was sick for an unrelated cause.) That’s 90% infected, which certainly gets your attention.

So now you send the rangers out to find more sick deer, and they eventually bring you 100 sick dear, of whom 50 test positive for BS-19. This is only 50% instead of 90%, but 50 sick animals is pretty serious, so you get funding for a large population survey, and the rangers test 1000 deer at random, and 240 of them (24%) test positive.

These are not comparable samples. The first group of deer was so sick that the rangers spontaneously decided to bring them to your attention. The second group was selected according to a plan, but they were all recognizably sick. Only the third group was a random sample. So is the disease getting worse because more deer have it in each round of testing? Or is it getting better because a smaller percentage of deer have it each time? Or is the disease holding steady and only the testing methodology is changing? It’s really hard to tell.

That’s why El Gato Malo’s use of the sampling rate model is wrong: Covid-19 testing (SARS-Cov-2 to be pedantic) in the United States has not been a clean and tidy random sampling process. It’s been a messy collection of testing and reporting policies that differ between locations and between different time periods in the evolution of the epidemic. And with the exception of screening and survey testing, most of the early techniques were highly motivated to find infected people, because those are the people in need of treatment and quarantine.

Testing began with emergency room doctors testing patients with severe respiratory infections to determine a course of treatment. Many of these tests were positive, because doctors were testing people they had identified as probably having Covid-19. As more tests became available, doctors began testing patients with milder symptoms, in the hope of catching the problem earlier. Eventually, they started testing people who had merely been exposed, even if they had no symptoms at all. Pretty soon test-and-trace teams began actively looking for people with Covid-19, and hospitals began testing all patients as a matter of course. In many places, you can now get tested simply by asking, and a number of companies are routinely testing their employees. Eventually (I hope), we will be doing over 100 million tests per month, and nearly all of them will come back negative. At some point, you’ve found all the cases, and no amount of testing can change that.

The point is, Covid-19 testing has been subject to decreasing returns. The more tests we do, the more positive results we’ll get, but each increase in testing produces a smaller increase in positive tests. When we first started getting test statistics, it only took about 4 or 5 tests to find a new case. Today it takes about 20 tests to find each new case of Covid-19. In some places, like New York State, it takes over 100 tests to find a single new case of Covid-19.

This means you can’t just blindly do linear extrapolation like the cat is trying to do. We don’t know the math governing this particular example of diminishing returns, because the situation is so complicated and we have no direct evidence of the correct answers, so there is no simple theoretical way to relate testing volume to the prevalence of the disease.

An arguably better approach is to use transmission dynamics modeling to model the spread of the disease, and back-project to estimate historic data. For example, using historic death rates, which we do have, the IHME model’s back-projection of the true infection rate looks like this:

That looks a bit like El Gato Malo’s estimate, with the first peak worse than the second. On the other hand, here’s a different back projection from the MIT model, which has the second peak as more severe:

Which one is right? I don’t know. You could argue that the IHME infected curve is a better fit to the historic death curve, but you could also argue that the MIT model has a better track record of making predictions, which is the true test of a model. And there are other models besides these two.

Make no mistake, I think el gato malo is right about the big picture: Some of the increase in cases is due to an increase in testing, so the summer peak isn’t as much worse than the spring peak as it might seem. But remember, no increase in testing can create Covid-19 cases that aren’t there. The summer peak is not an illusion that is better than it appears because of increased testing. The spring peak was the illusion, and it was worse than it appeared, because we didn’t have the ability to find cases as thoroughly as we do now.

If you’re commenting on Covid-19 news, as the cat and I are, it makes sense to show model outputs and present arguments based on them. But I don’t think objective news sources (or public health agencies) should be reporting unproven models as if they were facts. News sources owe it to their customers to report accurate and objective raw data. Leave the interpretation to somebody else.

(Personally, in my weekly Covid-19 stats tweetstorms, I almost never show charts of raw case rates without showing testing data somewhere nearby, and usually positivity as well, so people can reach their own conclusions. I am considered trying to calculate some model outputs, such as number of people currently infectious, but I’ve so far managed to resist the temptation.)

This post by Mark Draughn at Windypundit was originally published at The difference between data and a model

UIUC had predicted a rise in COVID-19 cases when students began moving into dorms last month, but thought it would be able to identify, isolate and snuff out the virus with the school’s frequent testing and quarantine requirements. UIUC has performed about 182,060 saliva tests since the technology was unveiled in early July.

The UIUC testing program was so massive that when the full student population was present it accounted for more than 1.5% of all testing in the United States.

But now UIUC is reporting over 700 people testing positive for the Covid-19 virus, and they are getting some grief because the models were not created by epidemiologists, but by a pair of physicists who supposedly disparaged epidemiology as “not intellectually challenging” (or maybe “thrilling”).

But the UIUC decision to use physicists as modelers is getting some support from a surprising source: Epidemiological modelers.

https://twitter.com/GermsAndNumbers/status/1301680043358261248

Lofgren goes on to argue, basically, that

• Plenty of epidemiologists don’t know how to build models.
• Epidemiological modeling has a lot in common with other kinds of modeling.
• The physicists building the models consulted with epidemiologists.
• It’s not surprising that people who chose to work on one science (physics) weren’t excited about working on another (epidemiology), but that doesn’t mean they didn’t do a good job.

So what went wrong? The short answer is that while the models may be simple, reality is really complex and weird.

Long ago, I used to write software for a company that built train simulators that we sold to railroads for training their engineers. I remember that one of our customers wanted us to prove that the models used in our simulator were accurate. Our modeling teams tried explaining how the models were based on scientific studies of train behavior and engineering data about specific components, but the customer wanted us to test our simulator against a real train on real track.

Having dealt with this request before, our modelers knew how to respond. They patiently listed out all the data the railroad would have to provide from their real train for us to setup the simulation model to match:

• The number of locomotives and cars in the train.
• The exact model of every locomotive and the options installed.
• The length and weight of every car.
• The amount of slack in the coupling between the cars.
• The exact model of brake valve used on every car.
• Were all those brake cylinders working? (It’s almost certain that in any long train, some of the brakes on some of the wheels aren’t actually doing anything useful.)
• What’s the coefficient of dynamic friction for the brakes on each car? (I.e. How worn out are they?)
• Locomotives use a diesel engine to generate electricity to run electric traction motors on each axle. Were all those motors working at full capacity or were some of them old and in need of service? Were you even sure they were all actually working? (More likely to be working than all the brakes, but it’s not unheard of for traction motors to be out.)
• The grade (percentage of incline) of every piece of track over which the train would be running.
• The degree of curvature and superelevation (tilt of the track from one side to the other) of every piece of track.
• Some measure of the quality of the track (I can’t remember how we did that).
• Were any parts of the track wet?
• Video of the engineer operating the control console so we can get timing data for each control input.

And so on. The request for whole-train validation was unceremoniously dropped.

Accurate modeling of train control systems and in-train physics can be surprisingly complicated. I don’t know a lot about epidemiological models, but I do know that they involve humans, so I’m guessing they are modeling a real world which is even more complicated than a train. That certainly seems to be the problem at UIUC:

But Nigel Goldenfeld, a physics professor who helped the school with modeling, said UIUC’s predictions did not take into account the level of noncompliance seen among students in recent weeks. The models did assume that some students would party, go to bars and fail to wear masks.

“What is not in the models is that students would actually fail to isolate,” he said. “That they would not respond to methods to reach them by (the public health department). That they would go to a party even if they knew they were COVID positive, or that they would host a party when they were COVID positive.”

It’s tempting to laugh at them for not realizing that college students would be irresponsible, but they did account for irresponsibility and include it in the model. They just underestimated how much the students would be irresponsible. Building the model is the easy part. It’s coming up with the inputs to the model that is so difficult.

This follows a pattern we’ve seen throughout attempts to model the Covid-19 pandemic: The spread of the disease itself follows some simple rules of physics and biology which can to some extent be captured in a dynamics model. The behavior of human beings…that’s a lot more complicated and unpredictable. It’s the people, not the disease, that make epidemiological modeling of this pandemic so hard to get right.

This post by Mark Draughn at Windypundit was originally published at Building the Model is the Easy Part

To be clear, I wouldn’t much care who else signed it. Signing a statement like this signals an agreement with the terms of the statement, not with everyone else who signed it. This doesn’t mean you should never check who else is signing something you’re asked to sign, because if all the other signers have some well-recognized affiliation — the Democratic Party, tech entrepreneurs, Juggalos — signing the statement could give other people the false impression that you’re a member of those groups when you’re not. But in this case, the list of signatories is pretty diverse, so I wouldn’t be too concerned.

The letter begins, as these things often do, with a recitation of claims, and I guess that’s the first of my concerns.

Our cultural institutions are facing a moment of trial. Powerful protests for racial and social justice are leading to overdue demands for police reform, along with wider calls for greater equality and inclusion across our society, not least in higher education, journalism, philanthropy, and the arts. But this needed reckoning has also intensified a new set of moral attitudes and political commitments that tend to weaken our norms of open debate and toleration of differences in favor of ideological conformity.

See, I’m not so sure about that. I’m certainly hearing more about “cancel culture” these days than I used to, and I keep hearing about questionable incidents of employers being pressured to fire people for things they’ve said, but I don’t know if that represents an actual change in activity, or if I’m just hearing more about it because it has upset some people with powerful platforms from which to complain.

It’s not like we haven’t seen that kind of exaggeration before. There was once a time when many serious people believed that Satan worshipers had infiltrated daycare centers and were abusing children in ritual ceremonies. Even today we have people who believe the U.S. suffers from widespread sex slavery, or that secret cabals of pederasts are being harbored by the Democratic party. Many people believe there is rampant tampering with Halloween candy, and parents have long worried that their children are being corrupted by innovations such as video games, rock music, and novels.

These are examples of moral panics, which usually involve exaggerated or wholly imaginary threats to our way of life. And I’m not sure how to tell if concerns about “cancel culture” are justified, or if they are just a different flavor of moral panic. I’m not saying “cancellations” don’t happen, but I’m not convinced things are getting terribly worse. I’m hearing a lot more about it, but it’s a major issue in the culture war and this is, after all, an election year.

But resistance must not be allowed to harden into its own brand of dogma or coercion—which right-wing demagogues are already exploiting. The democratic inclusion we want can be achieved only if we speak out against the intolerant climate that has set in on all sides.

This seems reasonable, with the understanding that just because all sides include intolerant assholes and thugs doesn’t mean that all sides are the same. Values still matter.

The free exchange of information and ideas, the lifeblood of a liberal society, is daily becoming more constricted.

Here’s the thing: The free exchange of information and ideas, the lifeblood of a liberal society, has never been greater than in the last decade or so. From the free speech revolution of the 1960s, to the development of the World Wide Web, to the explosion of low-overhead online publishing and social media, we have more freedom of exchange of information and ideas than at any point in history. I’m not ruling out the possibility that our culture is changing and our freedom of speech is becoming more restricted, but that’s only in comparison to the amazing level of free speech we have achieved. We might be sliding down from the top of the free speech mountain, but we’re still just below the summit.

I believe a big part of the problem is that everyone’s speech is more visible to everyone else. For example, I am nobody on Twitter, and I still had a tweet last week that was seen by 96,000 people. All of us have the opportunity to be heard by more people, which means we can also piss off more people.

So when you hear of some random politician or minor celebrity getting cancelled for saying something offensive, remember that 20 years ago he would have said that offensive thing to a few people at a party, who might have repeated it to a few other people at other parties, and that would be it. But in our modern age, that guy will tweet out his dumbass opinion to his thousands of followers, who will retweet it to thousands more, and so on, until 20 million Twitter users are outraged at him.

Furthermore, each of those millions of people also has access to social media. Twenty years ago, even if word got out that some politician or minor celebrity had said something offensive, the people who got offended would have complained about it to their friends and family, and maybe at social gatherings. But now they can complain on social media, where the offending celebrity can, for the first time in history, see it for themselves. As can thousands of other people, who will retweet it to thousands more, and so on.

It’s now much more difficult to ignore what people are saying about you. You get a lot more pushback, and from a lot more really angry people, when your offensive comment reaches a thousand times more people. That’s doesn’t mean you have less speech. Rather, it’s the natural consequence of you and everybody else having more speech.

While we have come to expect this on the radical right,

Some critics of the letter have been complaining about this clause, because “cancel culture” and “political correctness” are left-wing phenomena, coming from academia and the press. But the right has its own political correctness. It just takes different forms. If you don’t believe me, ask some people on the right how they feel about flag burning, or disrespecting members of the military.

There’s also the post-9/11 backlash against people who objected to the existence and execution of the war on terror. And we have police officers getting fired for online comments that do not support the department, and the accusation that politicians who support Black Lives Matter, or fail to completely defend the police, are therefore police-haters who support Antifa. And let’s not forget all the peaceful protesters over the past few weeks who have been assaulted by police with little provocation or under thin pretexts. And the right’s never-ending attacks on “the media.” And whatever authoritarian bullshit this is.

We uphold the value of robust and even caustic counter-speech from all quarters.

Finally, a clear statement of values, and one I support 100%. It’s why I got into reading (and writing) blogs.

But it is now all too common to hear calls for swift and severe retribution in response to perceived transgressions of speech and thought. More troubling still, institutional leaders, in a spirit of panicked damage control, are delivering hasty and disproportionate punishments instead of considered reforms. Editors are fired for running controversial pieces; books are withdrawn for alleged inauthenticity; journalists are barred from writing on certain topics; professors are investigated for quoting works of literature in class; a researcher is fired for circulating a peer-reviewed academic study; and the heads of organizations are ousted for what are sometimes just clumsy mistakes.

This is such a scattershot list of grievances that I can’t some up with a single coherent evaluation. The devil is in the details, particularly in the details of the roles that these people play at the institutions that are punishing them. Academic institutions should thrive on a diversity of ideas and opinions. Their leaders should expect researchers, professors, and students to ask provocative questions and arrive at unpleasant answers. This will inevitably lead to difficult confrontations, especially since there always seem to be a few highly eccentric academics who go completely off the rails and embarrass the institution. But it’s the price you pay when you support academic freedom. Institutions that promise freedom and fail to deliver are run by cowards.

A similar argument applies to journalism and other forums for expressing opinions. A broad acceptance of different viewpoints will serve them well, and their leaders have an obligation to support their contributors. And yet publications surely have a right to establish an editorial viewpoint. OANN has a right to kick out commentators who don’t support President Trump, Jacobin has a right to kick out those who don’t support socialism, Reason has can kick out non-libertarians, and Everyday Feminism can kick out people who don’t support…whatever brand of crazy they sell there.

The point is, every business and institution has some right to demand certain standards from the people they pay to represent them. If a spokesperson or executive makes the company look bad, the company has a right to do something about that. Corporations, charities, and churches have images to preserve and values to uphold, and it’s legitimate for them to terminate employees who obstruct their goals.

Whatever the arguments around each particular incident, the result has been to steadily narrow the boundaries of what can be said without the threat of reprisal. We are already paying the price in greater risk aversion among writers, artists, and journalists who fear for their livelihoods if they depart from the consensus, or even lack sufficient zeal in agreement.

Like I said…maybe.

Speaking for myself, there are definitely some topics I’ve declined to blog about out of concern for my employment. When I started this blog, I was an independent software consultant, and I quickly developed a devil-may-care attitude about reactions to my writing. That changed a few years ago, however, when I went back to regular full-time work. I became more conscious of the fact that my words could reflect on my employer. At that time, my employer was Thomson-Reuters, which includes the Reuters news agency, and that led me to believe (perhaps correctly) that the company would tend to have some respect for my freedom of speech. (The employee handbook also suggest this.) In any case, my blog had been waning in influence for years, and the issue never arose.

This stifling atmosphere will ultimately harm the most vital causes of our time. The restriction of debate, whether by a repressive government or an intolerant society, invariably hurts those who lack power and makes everyone less capable of democratic participation. The way to defeat bad ideas is by exposure, argument, and persuasion, not by trying to silence or wish them away.

Within the limits of my earlier remarks about organizations having a right to control the message they send, I certainly agree that a “stifling atmosphere will ultimately harm the most vital causes of our time.” And the best response to a bad idea is a good one.

We refuse any false choice between justice and freedom, which cannot exist without each other. As writers we need a culture that leaves us room for experimentation, risk taking, and even mistakes. We need to preserve the possibility of good-faith disagreement without dire professional consequences.

This is the only call for action in the letter. And for the record, I agree with the principles.

Nevertheless, after all the hype, I find myself disappointed. I guess my main impression is that for all the attention this letter has attracted — and for all the prominent writers who signed on — it doesn’t actually have much to say. Basically, it boils down to a bunch of assertions about the existence of “cancel culture,” ending with a vague request for “less of this, please.”

I’m not saying I could do any better, and I imagine that’s what you get when what you need a statement that appeals to a broad range of signatories. Still, for all the fuss, I expected something more profound.

This post by Mark Draughn at Windypundit was originally published at Much ado about the Harper’s letter

So the other day, my wife and I were at McDonald’s, and we had our food and were sitting at our table, and I went to the soda dispenser to fill my cup with Diet Coke, and as I got there, I noticed two things. First, there was a Plexiglas shield over the dispenser area. Second, as I got to the dispenser, a young girl who was approaching at the same time suddenly stopped and backed away. That’s when I realized I wasn’t wearing a mask. As I turned back to the table, I realized my wife wasn’t wearing her mask either, and neither were the people at any of the adjacent tables! Oh crap, we had to get our masks on —

And then I woke up.

Fuck. Now I’m having coronavirus dreams. 

This post by Mark Draughn at Windypundit was originally published at Corona Dreaming

CCHTTNAACTTTCGATCTCTTGTAGATCTGTTCTCTAAACGAACTTTAAAATCTGTGTGGCTGTCACTCG
GCTGCATGCTTAGTGCACTCACGCAGTATAATTAATAACTAATTACTGTCGTTGACAGGACACGAGTAAC
TCGTCTATCTTCTGCAGGCTGCTTACGGTTTCGTCCGTGTTGCAGCCGATCATCAGCACATCTAGGTTTT
GTCCGGGTGTGACCGAAAGGTAAGATGGAGAGCCTTGTCCCTGGTTTCAACGAGAAAACACACGTCCAAC
TCAGTTTGCCTGTTTTACAGGTTCGCGACGTGCTCGTACGTGGCTTTGGAGACTCCGTGGAGGAGGTCTT
ATCAGAGGCACGTCAACATCTTAAAGATGGCACTTGTGGCTTAGTAGAAGTTGAAAAAGGCGTTTTGCCT
CAACTTGAACAGCCCTATGTGTTCATCAAACGTTCGGATGCTCGAACTGCACCTCATGGTCATGTTATGG
TTGAGCTGGTAGCAGAACTCGAAGGCATTCAGTACGGTCGTAGTGGTGAGACACTTGGTGTCCTTGTCCC
TCATGTGGGCGAAATACCAGTGGCTTACCGCAAGGTTCTTCTTCGTAAGAACGGTAATAAAGGAGCTGGT
GGCCATAGTTACGGCGCCGATCTAAAGTCATTTGACTTAGGCGACGAGCTTGGCACTGATCCTTATGAAG
ATTTTCAAGAAAACTGGAACACTAAACATAGCAGTGGTGTTACCCGTGAACTCATGCGTGAGCTTAACGG
AGGGGCATACACTCGCTATGTCGATAACAACTTCTGTGGCCCTGATGGCTACCCTCTTGAGTGCATTAAA
GACCTTCTAGCACGTGCTGGTAAAGCTTCATGCACTTTGTCCGAACAACTGGACTTTATTGACACTAAGA
GGGGTGTATACTGCTGCCGTGAACATGAGCATGAAATTGCTTGGTACACGGAACGTTCTGAAAAGAGCTA
TGAATTGCAGACACCTTTTGAAATTAAATTGGCAAAGAAATTTGACACCTTCAATGGGGAATGTCCAAAT
TTTGTATTTCCCTTAAATTCCATAATCAAGACTATTCAACCAAGGGTTGAAAAGAAAAAGCTTGATGGCT
TTATGGGTAGAATTCGATCTGTCTATCCAGTTGCGTCACCAAATGAATGCAACCAAATGTGCCTTTCAAC
TCTCATGAAGTGTGATCATTGTGGTGAAACTTCATGGCAGACGGGCGATTTTGTTAAAGCCACTTGCGAA
TTTTGTGGCACTGAGAATTTGACTAAAGAAGGTGCCACTACTTGTGGTTACTTACCCCAAAATGCTGTTG
TTAAAATTTATTGTCCAGCATGTCACAATTCAGAAGTAGGACCTGAGCATAGTCTTGCCGAATACCATAA
TGAATCTGGCTTGAAAACCATTCTTCGTAAGGGTGGTCGCACTATTGCCTTTGGAGGCTGTGTGTTCTCT
TATGTTGGTTGCCATAACAAGTGTGCCTATTGGGTTCCACGTGCTAGCGCTAACATAGGTTGTAACCATA
CAGGTGTTGTTGGAGAAGGTTCCGAAGGTCTTAATGACAACCTTCTTGAAATACTCCAAAAAGAGAAAGT
CAACATCAATATTGTTGGTGACTTTAAACTTAATGAAGAGATCGCCATTATTTTGGCATCTTTTTCTGCT
TCCACAAGTGCTTTTGTGGAAACTGTGAAAGGTTTGGATTATAAAGCATTCAAACAAATTGTTGAATCCT
GTGGTAATTTTAAAGTTACAAAAGGAAAAGCTAAAAAAGGTGCCTGGAATATTGGTGAACAGAAATCAAT
ACTGAGTCCTCTTTATGCATTTGCATCAGAGGCTGCTCGTGTTGTACGATCAATTTTCTCCCGCACTCTT
GAAACTGCTCAAAATTCTGTGCGTGTTTTACAGAAGGCCGCTATAACAATACTAGATGGAATTTCACAGT
ATTCACTGAGACTCATTGATGCTATGATGTTCACATCTGATTTGGCTACTAACAATCTAGTTGTAATGGC
CTACATTACAGGTGGTGTTGTTCAGTTGACTTCGCAGTGGCTAACTAACATCTTTGGCACTGTTTATGAA
AAACTCAAACCCGTCCTTGATTGGCTTGAAGAGAAGTTTAAGGAAGGTGTAGAGTTTCTTAGAGACGGTT
GGGAAATTGTTAAATTTATCTCAACCTGTGCTTGTGAAATTGTCGGTGGACAAATTGTCACCTGTGCAAA
GGAAATTAAGGAGAGTGTTCAGACATTCTTTAAGCTTGTAAATAAATTTTTGGCTTTGTGTGCTGACTCT
ATCATTATTGGTGGAGCTAAACTTAAAGCCTTGAATTTAGGTGAAACATTTGTCACGCACTCAAAGGGAT
TGTATAGAAAGTGTGTTAAATCCAGAGAAGAAACTGGCCTACTCATGCCTCTAAAAGCCCCAAAAGAAAT
TATCTTCTTAGAGGGAGAAACACTTCCCACAGAAGTGTTAACAGAGGAAGTTGTCTTGAAAACTGGTGAT
TTACAACCATTAGAACAACCTACTAGTGAAGCTGTTGAAGCTCCATTGGTTGGTACACCAGTTTGTATTA
ACGGGCTTATGTTGCTCGAAATCAAAGACACAGAAAAGTACTGTGCCCTTGCACCTAATATGATGGTAAC
AAACAATACCTTCACACTCAAAGGCGGTGCACCAACAAAGGTTACTTTTGGTGATGACACTGTGATAGAA
GTGCAAGGTTACAAGAGTGTGAATATCACTTTTGAACTTGATGAAAGGATTGATAAAGTACTTAATGAGA
AGTGCTCTGCCTATACAGTTGAACTCGGTACAGAAGTAAATGAGTTCGCCTGTGTTGTGGCAGATGCTGT
CATAAAAACTTTGCAACCAGTATCTGAATTACTTACACCACTGGGCATTGATTTAGATGAGTGGAGTATG
GCTACATACTACTTATTTGATGAGTCTGGTGAGTTTAAATTGGCTTCACATATGTATTGTTCTTTTTACC
CTCCAGATGAGGATGAAGAAGAAGGTGATTGTGAAGAAGAAGAGTTTGAGCCATCAACTCAATATGAGTA
TGGTACTGAAGATGATTACCAAGGTAAACCTTTGGAATTTGGTGCCACTTCTGCTGCTCTTCAACCTGAA
GAAGAGCAAGAAGAAGATTGGTTAGATGATGATAGTCAACAAACTGTTGGTCAACAAGACGGCAGTGAGG
ACAATCAGACAACTACTATTCAAACAATTGTTGAGGTTCAACCTCAATTAGAGATGGAACTTACACCAGT
TGTTCAGACTATTGAAGTGAATAGTTTTAGTGGTTATTTAAAACTTACTGACAATGTATACATTAAAAAT
GCAGACATTGTGGAAGAAGCTAAAAAGGTAAAACCAACAGTGGTTGTTAATGCAGCCAATGTTTACCTTA
AACATGGAGGAGGTGTTGCAGGAGCCTTAAATAAGGCTACTAACAATGCCATGCAAGTTGAATCTGATGA
TTACATAGCTACTAATGGACCACTTAAAGTGGGTGGTAGTTGTGTTTTAAGCGGACACAATCTTGCTAAA
CACTGTCTTCATGTTGTCGGCCCAAATGTTAACAAAGGTGAAGACATTCAACTTCTTAAGAGTGCTTATG
AAAATTTTAATCAGCACGAAGTTCTACTTGCACCATTATTATCAGCTGGTATTTTTGGTGCTGACCCTAT
ACATTCTTTAAGAGTTTGTGTAGATACTGTTCGCACAAATGTCTACTTAGCTGTCTTTGATAAAAATCTC
TATGACAAACTTGTTTCAAGCTTTTTGGAAATGAAGAGTGAAAAGCAAGTTGAACAAAAGATCGCTGAGA
TTCCTAAAGAGGAAGTTAAGCCATTTATAACTGAAAGTAAACCTTCAGTTGAACAGAGAAAACAAGATGA
TAAGAAAATCAAAGCTTGTGTTGAAGAAGTTACAACAACTCTGGAAGAAACTAAGTTCCTCACAGAAAAC
TTGTTACTTTATATTGACATTAATGGCAATCTTCATCCAGATTCTGCCACTCTTGTTAGTGACATTGACA
TCACTTTCTTAAAGAAAGATGCTCCATATATAGTGGGTGATGTTGTTCAAGAGGGTGTTTTAACTGCTGT
GGTTATACCTACTAAAAAGGCTGGTGGCACTACTGAAATGCTAGCGAAAGCTTTGAGAAAAGTGCCAACA
GACAATTATATAACCACTTACCCGGGTCAGGGTTTAAATGGTTACACTGTAGAGGAGGCAAAGACAGTGC
TTAAAAAGTGTAAAAGTGCCTTTTACATTCTACCATCTATTATCTCTAATGAGAAGCAAGAAATTCTTGG
AACTGTTTCTTGGAATTTGCGAGAAATGCTTGCACATGCAGAAGAAACACGCAAATTAATGCCTGTCTGT
GTGGAAACTAAAGCCATAGTTTCAACTATACAGCGTAAATATAAGGGTATTAAAATACAAGAGGGTGTGG
TTGATTATGGTGCTAGATTTTACTTTTACACCAGTAAAACAACTGTAGCGTCACTTATCAACACACTTAA
CGATCTAAATGAAACTCTTGTTACAATGCCACTTGGCTATGTAACACATGGCTTAAATTTGGAAGAAGCT
GCTCGGTATATGAGATCTCTCAAAGTGCCAGCTACAGTTTCTGTTTCTTCACCTGATGCTGTTACAGCGT
ATAATGGTTATCTTACTTCTTCTTCTAAAACACCTGAAGAACATTTTATTGAAACCATCTCACTTGCTGG
TTCCTATAAAGATTGGTCCTATTCTGGACAATCTACACAACTAGGTATAGAATTTCTTAAGAGAGGTGAT
AAAAGTGTATATTACACTAGTAATCCTACCACATTCCACCTAGATGGTGAAGTTATCACCTTTGACAATC
TTAAGACACTTCTTTCTTTGAGAGAAGTGAGGACTATTAAGGTGTTTACAACAGTAGACAACATTAACCT
CCACACGCAAGTTGTGGACATGTCAATGACATATGGACAACAGTTTGGTCCAACTTATTTGGATGGAGCT
GATGTTACTAAAATAAAACCTCATAATTCACATGAAGGTAAAACATTTTATGTTTTACCTAATGATGACA
CTCTACGTGTTGAGGCTTTTGAGTACTACCACACAACTGATCCTAGTTTTCTGGGTAGGTACATGTCAGC
ATTAAATCACACTAAAAAGTGGAAATACCCACAAGTTAATGGTTTAACTTCTATTAAATGGGCAGATAAC
AACTGTTATCTTGCCACTGCATTGTTAACACTCCAACAAATAGAGTTGAAGTTTAATCCACCTGCTCTAC
AAGATGCTTATTACAGAGCAAGGGCTGGTGAAGCTGCTAACTTTTGTGCACTTATCTTAGCCTACTGTAA
TAAGACAGTAGGTGAGTTAGGTGATGTTAGAGAAACAATGAGTTACTTGTTTCAACATGCCAATTTAGAT
TCTTGCAAAAGAGTCTTGAACGTGGTGTGTAAAACTTGTGGACAACAGCAGACAACCCTTAAGGGTGTAG
AAGCTGTTATGTACATGGGCACACTTTCTTATGAACAATTTAAGAAAGGTGTTCAGATACCTTGTACGTG
TGGTAAACAAGCTACAAAATATCTAGTACAACAGGAGTCACCTTTTGTTATGATGTCAGCACCACCTGCT
CAGTATGAACTTAAGCATGGTACATTTACTTGTGCTAGTGAGTACACTGGTAATTACCAGTGTGGTCACT
ATAAACATATAACTTCTAAAGAAACTTTGTATTGCATAGACGGTGCTTTACTTACAAAGTCCTCAGAATA
CAAAGGTCCTATTACGGATGTTTTCTACAAAGAAAACAGTTACACAACAACCATAAAACCAGTTACTTAT
AAATTGGATGGTGTTGTTTGTACAGAAATTGACCCTAAGTTGGACAATTATTATAAGAAAGACAATTCTT
ATTTCACAGAGCAACCAATTGATCTTGTACCAAACCAACCATATCCAAACGCAAGCTTCGATAATTTTAA
GTTTGTATGTGATAATATCAAATTTGCTGATGATTTAAACCAGTTAACTGGTTATAAGAAACCTGCTTCA
AGAGAGCTTAAAGTTACATTTTTCCCTGACTTAAATGGTGATGTGGTGGCTATTGATTATAAACACTACA
CACCCTCTTTTAAGAAAGGAGCTAAATTGTTACATAAACCTATTGTTTGGCATGTTAACAATGCAACTAA
TAAAGCCACGTATAAACCAAATACCTGGTGTATACGTTGTCTTTGGAGCACAAAACCAGTTGAAACATCA
AATTCGTTTGATGTACTGAAGTCAGAGGACGCGCAGGGAATGGATAATCTTGCCTGCGAAGATCTAAAAC
CAGTCTCTGAAGAAGTAGTGGAAAATCCTACCATACAGAAAGACGTTCTTGAGTGTAATGTGAAAACTAC
CGAAGTTGTAGGAGACATTATACTTAAACCAGCAAATAATAGTTTAAAAATTACAGAAGAGGTTGGCCAC
ACAGATCTAATGGCTGCTTATGTAGACAATTCTAGTCTTACTATTAAGAAACCTAATGAATTATCTAGAG
TATTAGGTTTGAAAACCCTTGCTACTCATGGTTTAGCTGCTGTTAATAGTGTCCCTTGGGATACTATAGC
TAATTATGCTAAGCCTTTTCTTAACAAAGTTGTTAGTACAACTACTAACATAGTTACACGGTGTTTAAAC
CGTGTTTGTACTAATTATATGCCTTATTTCTTTACTTTATTGCTACAATTGTGTACTTTTACTAGAAGTA
CAAATTCTAGAATTAAAGCATCTATGCCGACTACTATAGCAAAGAATACTGTTAAGAGTGTCGGTAAATT
TTGTCTAGAGGCTTCATTTAATTATTTGAAGTCACCTAATTTTTCTAAACTGATAAATATTATAATTTGG
TTTTTACTATTAAGTGTTTGCCTAGGTTCTTTAATCTACTCAACCGCTGCTTTAGGTGTTTTAATGTCTA
ATTTAGGCATGCCTTCTTACTGTACTGGTTACAGAGAAGGCTATTTGAACTCTACTAATGTCACTATTGC
AACCTACTGTACTGGTTCTATACCTTGTAGTGTTTGTCTTAGTGGTTTAGATTCTTTAGACACCTATCCT
TCTTTAGAAACTATACAAATTACCATTTCATCTTTTAAATGGGATTTAACTGCTTTTGGCTTAGTTGCAG
AGTGGTTTTTGGCATATATTCTTTTCACTAGGTTTTTCTATGTACTTGGATTGGCTGCAATCATGCAATT
GTTTTTCAGCTATTTTGCAGTACATTTTATTAGTAATTCTTGGCTTATGTGGTTAATAATTAATCTTGTA
CAAATGGCCCCGATTTCAGCTATGGTTAGAATGTACATCTTCTTTGCATCATTTTATTATGTATGGAAAA
GTTATGTGCATGTTGTAGACGGTTGTAATTCATCAACTTGTATGATGTGTTACAAACGTAATAGAGCAAC
AAGAGTCGAATGTACAACTATTGTTAATGGTGTTAGAAGGTCCTTTTATGTCTATGCTAATGGAGGTAAA
GGCTTTTGCAAACTACACAATTGGAATTGTGTTAATTGTGATACATTCTGTGCTGGTAGTACATTTATTA
GTGATGAAGTTGCGAGAGACTTGTCACTACAGTTTAAAAGACCAATAAATCCTACTGACCAGTCTTCTTA
CATCGTTGATAGTGTTACAGTGAAGAATGGTTCCATCCATCTTTACTTTGATAAAGCTGGTCAAAAGACT
TATGAAAGACATTCTCTCTCTCATTTTGTTAACTTAGACAACCTGAGAGCTAATAACACTAAAGGTTCAT
TGCCTATTAATGTTATAGTTTTTGATGGTAAATCAAAATGTGAAGAATCATCTGCAAAATCAGCGTCTGT
TTACTACAGTCAGCTTATGTGTCAACCTATACTGTTACTAGATCAGGCATTAGTGTCTGATGTTGGTGAT
AGTGCGGAAGTTGCAGTTAAAATGTTTGATGCTTACGTTAATACGTTTTCATCAACTTTTAACGTACCAA
TGGAAAAACTCAAAACACTAGTTGCAACTGCAGAAGCTGAACTTGCAAAGAATGTGTCCTTAGACAATGT
CTTATCTACTTTTATTTCAGCAGCTCGGCAAGGGTTTGTTGATTCAGATGTAGAAACTAAAGATGTTGTT
GAATGTCTTAAATTGTCACATCAATCTGACATAGAAGTTACTGGCGATAGTTGTAATAACTATATGCTCA
CCTATAACAAAGTTGAAAACATGACACCCCGTGACCTTGGTGCTTGTATTGACTGTAGTGCGCGTCATAT
TAATGCGCAGGTAGCAAAAAGTCACAACATTGCTTTGATATGGAACGTTAAAGATTTCATGTCATTGTCT
GAACAACTACGAAAACAAATACGTAGTGCTGCTAAAAAGAATAACTTACCTTTTAAGTTGACATGTGCAA
CTACTAGACAAGTTGTTAATGTTGTAACAACAAAGATAGCACTTAAGGGTGGTAAAATTGTTAATAATTG
GTTGAAGCAGTTAATTAAAGTTACACTTGTGTTCCTTTTTGTTGCTGCTATTTTCTATTTAATAACACCT
GTTCATGTCATGTCTAAACATACTGACTTTTCAAGTGAAATCATAGGATACAAGGCTATTGATGGTGGTG
TCACTCGTGACATAGCATCTACAGATACTTGTTTTGCTAACAAACATGCTGATTTTGACACATGGTTTAG
CCAGCGTGGTGGTAGTTATACTAATGACAAAGCTTGCCCATTGATTGCTGCAGTCATAACAAGAGAAGTG
GGTTTTGTCGTGCCTGGTTTGCCTGGCACGATATTACGCACAACTAATGGTGACTTTTTGCATTTCTTAC
CTAGAGTTTTTAGTGCAGTTGGTAACATCTGTTACACACCATCAAAACTTATAGAGTACACTGACTTTGC
AACATCAGCTTGTGTTTTGGCTGCTGAATGTACAATTTTTAAAGATGCTTCTGGTAAGCCAGTACCATAT
TGTTATGATACCAATGTACTAGAAGGTTCTGTTGCTTATGAAAGTTTACGCCCTGACACACGTTATGTGC
TCATGGATGGCTCTATTATTCAATTTCCTAACACCTACCTTGAAGGTTCTGTTAGAGTGGTAACAACTTT
TGATTCTGAGTACTGTAGGCACGGCACTTGTGAAAGATCAGAAGCTGGTGTTTGTGTATCTACTAGTGGT
AGATGGGTACTTAACAATGATTATTACAGATCTTTACCAGGAGTTTTCTGTGGTGTAGATGCTGTAAATT
TACTTACTAATATGTTTACACCACTAATTCAACCTATTGGTGCTTTGGACATATCAGCATCTATAGTAGC
TGGTGGTATTGTAGCTATCGTAGTAACATGCCTTGCCTACTATTTTATGAGGTTTAGAAGAGCTTTTGGT
GAATACAGTCATGTAGTTGCCTTTAATACTTTACTATTCCTTATGTCATTCACTGTACTCTGTTTAACAC
CAGTTTACTCATTCTTACCTGGTGTTTATTCTGTTATTTACTTGTACTTGACATTTTATCTTACTAATGA
TGTTTCTTTTTTAGCACATATTCAGTGGATGGTTATGTTCACACCTTTAGTACCTTTCTGGATAACAATT
GCTTATATCATTTGTATTTCCACAAAGCATTTCTATTGGTTCTTTAGTAATTACCTAAAGAGACGTGTAG
TCTTTAATGGTGTTTCCTTTAGTACTTTTGAAGAAGCTGCGCTGTGCACCTTTTTGTTAAATAAAGAAAT
GTATCTAAAGTTGCGTAGTGATGTGCTATTACCTCTTACGCAATATAATAGATACTTAGCTCTTTATAAT
AAGTACAAGTATTTTAGTGGAGCAATGGATACAACTAGCTACAGAGAAGCTGCTTGTTGTCATCTCGCAA
AGGCTCTCAATGACTTCAGTAACTCAGGTTCTGATGTTCTTTACCAACCACCACAAACCTCTATCACCTC
AGCTGTTTTGCAGAGTGGTTTTAGAAAAATGGCATTCCCATCTGGTAAAGTTGAGGGTTGTATGGTACAA
GTAACTTGTGGTACAACTACACTTAACGGTCTTTGGCTTGATGACGTAGTTTACTGTCCAAGACATGTGA
TCTGCACCTCTGAAGACATGCTTAACCCTAATTATGAAGATTTACTCATTCGTAAGTCTAATCATAATTT
CTTGGTACAGGCTGGTAATGTTCAACTCAGGGTTATTGGACATTCTATGCAAAATTGTGTACTTAAGCTT
AAGGTTGATACAGCCAATCCTAAGACACCTAAGTATAAGTTTGTTCGCATTCAACCAGGACAGACTTTTT
CAGTGTTAGCTTGTTACAATGGTTCACCATCTGGTGTTTACCAATGTGCTATGAGGCCCAATTTCACTAT
TAAGGGTTCATTCCTTAATGGTTCATGTGGTAGTGTTGGTTTTAACATAGATTATGACTGTGTCTCTTTT
TGTTACATGCACCATATGGAATTACCAACTGGAGTTCATGCTGGCACAGACTTAGAAGGTAACTTTTATG
GACCTTTTGTTGACAGGCAAACAGCACAAGCAGCTGGTACGGACACAACTATTACAGTTAATGTTTTAGC
TTGGTTGTACGCTGCTGTTATAAATGGAGACAGGTGGTTTCTCAATCGATTTACCACAACTCTTAATGAC
TTTAACCTTGTGGCTATGAAGTACAATTATGAACCTCTAACACAAGACCATGTTGACATACTAGGACCTC
TTTCTGCTCAAACTGGAATTGCCGTTTTAGATATGTGTGCTTCATTAAAAGAATTACTGCAAAATGGTAT
GAATGGACGTACCATATTGGGTAGTGCTTTATTAGAAGATGAATTTACACCTTTTGATGTTGTTAGACAA
TGCTCAGGTGTTACTTTCCAAAGTGCAGTGAAAAGAACAATCAAGGGTACACACCACTGGTTGTTACTCA
CAATTTTGACTTCACTTTTAGTTTTAGTCCAGAGTACTCAATGGTCTTTGTTCTTTTTTTTGTATGAAAA
TGCCTTTTTACCTTTTGCTATGGGTATTATTGCTATGTCTGCTTTTGCAATGATGTTTGTCAAACATAAG
CATGCATTTCTCTGTTTGTTTTTGTTACCTTCTCTTGCCACTGTAGCTTATTTTAATATGGTCTATATGC
CTGCTAGTTGGGTGATGCGTATTATGACATGGTTGGATATGGTTGATACTAGTTTGTCTGGTTTTAAGCT
AAAAGACTGTGTTATGTATGCATCAGCTGTAGTGTTACTAATCCTTATGACAGCAAGAACTGTGTATGAT
GATGGTGCTAGGAGAGTGTGGACACTTATGAATGTCTTGACACTCGTTTATAAAGTTTATTATGGTAATG
CTTTAGATCAAGCCATTTCCATGTGGGCTCTTATAATCTCTGTTACTTCTAACTACTCAGGTGTAGTTAC
AACTGTCATGTTTTTGGCCAGAGGTATTGTTTTTATGTGTGTTGAGTATTGCCCTATTTTCTTCATAACT
GGTAATACACTTCAGTGTATAATGCTAGTTTATTGTTTCTTAGGCTATTTTTGTACTTGTTACTTTGGCC
TCTTTTGTTTACTCAACCGCTACTTTAGACTGACTCTTGGTGTTTATGATTACTTAGTTTCTACACAGGA
GTTTAGATATATGAATTCACAGGGACTACTCCCACCCAAGAATAGCATAGATGCCTTCAAACTCAACATT
AAATTGTTGGGTGTTGGTGGCAAACCTTGTATCAAAGTAGCCACTGTACAGTCTAAAATGTCAGATGTAA
AGTGCACATCAGTAGTCTTACTCTCAGTTTTGCAACAACTCAGAGTAGAATCATCATCTAAATTGTGGGC
TCAATGTGTCCAGTTACACAATGACATTCTCTTAGCTAAAGATACTACTGAAGCCTTTGAAAAAATGGTT
TCACTACTTTCTGTTTTGCTTTCCATGCAGGGTGCTGTAGACATAAACAAGCTTTGTGAAGAAATGCTGG
ACAACAGGGCAACCTTACAAGCTATAGCCTCAGAGTTTAGTTCCCTTCCATCATATGCAGCTTTTGCTAC
TGCTCAAGAAGCTTATGAGCAGGCTGTTGCTAATGGTGATTCTGAAGTTGTTCTTAAAAAGTTGAAGAAG
TCTTTGAATGTGGCTAAATCTGAATTTGACCGTGATGCAGCCATGCAACGTAAGTTGGAAAAGATGGCTG
ATCAAGCTATGACCCAAATGTATAAACAGGCTAGATCTGAGGACAAGAGGGCAAAAGTTACTAGTGCTAT
GCAGACAATGCTTTTCACTATGCTTAGAAAGTTGGATAATGATGCACTCAACAACATTATCAACAATGCA
AGAGATGGTTGTGTTCCCTTGAACATAATACCTCTTACAACAGCAGCCAAACTAATGGTTGTCATACCAG
ACTATAACACATATAAAAATACGTGTGATGGTACAACATTTACTTATGCATCAGCATTGTGGGAAATCCA
ACAGGTTGTAGATGCAGATAGTAAAATTGTTCAACTTAGTGAAATTAGTATGGACAATTCACCTAATTTA
GCATGGCCTCTTATTGTAACAGCTTTAAGGGCCAATTCTGCTGTCAAATTACAGAATAATGAGCTTAGTC
CTGTTGCACTACGACAGATGTCTTGTGCTGCCGGTACTACACAAACTGCTTGCACTGATGACAATGCGTT
AGCTTACTACAACACAACAAAGGGAGGTAGGTTTGTACTTGCACTGTTATCCGATTTACAGGATTTGAAA
TGGGCTAGATTCCCTAAGAGTGATGGAACTGGTACTATCTATACAGAACTGGAACCACCTTGTAGGTTTG
TTACAGACACACCTAAAGGTCCTAAAGTGAAGTATTTATACTTTATTAAAGGATTAAACAACCTAAATAG
AGGTATGGTACTTGGTAGTTTAGCTGCCACAGTACGTCTACAAGCTGGTAATGCAACAGAAGTGCCTGCC
AATTCAACTGTATTATCTTTCTGTGCTTTTGCTGTAGATGCTGCTAAAGCTTACAAAGATTATCTAGCTA
GTGGGGGACAACCAATCACTAATTGTGTTAAGATGTTGTGTACACACACTGGTACTGGTCAGGCAATAAC
AGTTACACCGGAAGCCAATATGGATCAAGAATCCTTTGGTGGTGCATCGTGTTGTCTGTACTGCCGTTGC
CACATAGATCATCCAAATCCTAAAGGATTTTGTGACTTAAAAGGTAAGTATGTACAAATACCTACAACTT
GTGCTAATGACCCTGTGGGTTTTACACTTAAAAACACAGTCTGTACCGTCTGCGGTATGTGGAAAGGTTA
TGGCTGTAGTTGTGATCAACTCCGCGAACCCATGCTTCAGTCAGCTGATGCACAATCGTTTTTAAACGGG
TTTGCGGTGTAAGTGCAGCCCGTCTTACACCGTGCGGCACAGGCACTAGTACTGATGTCGTATACAGGGC
TTTTGACATCTACAATGATAAAGTAGCTGGTTTTGCTAAATTCCTAAAAACTAATTGTTGTCGCTTCCAA
GAAAAGGACGAAGATGACAATTTAATTGATTCTTACTTTGTAGTTAAGAGACACACTTTCTCTAACTACC
AACATGAAGAAACAATTTATAATTTACTTAAGGATTGTCCAGCTGTTGCTAAACATGACTTCTTTAAGTT
TAGAATAGACGGTGACATGGTACCACATATATCACGTCAACGTCTTACTAAATACACAATGGCAGACCTC
GTCTATGCTTTAAGGCATTTTGATGAAGGTAATTGTGACACATTAAAAGAAATACTTGTCACATACAATT
GTTGTGATGATGATTATTTCAATAAAAAGGACTGGTATGATTTTGTAGAAAACCCAGATATATTACGCGT
ATACGCCAACTTAGGTGAACGTGTACGCCAAGCTTTGTTAAAAACAGTACAATTCTGTGATGCCATGCGA
AATGCTGGTATTGTTGGTGTACTGACATTAGATAATCAAGATCTCAATGGTAACTGGTATGATTTCGGTG
ATTTCATACAAACCACGCCAGGTAGTGGAGTTCCTGTTGTAGATTCTTATTATTCATTGTTAATGCCTAT
ATTAACCTTGACCAGGGCTTTAACTGCAGAGTCACATGTTGACACTGACTTAACAAAGCCTTACATTAAG
TGGGATTTGTTAAAATATGACTTCACGGAAGAGAGGTTAAAACTCTTTGACCGTTATTTTAAATATTGGG
ATCAGACATACCACCCAAATTGTGTTAACTGTTTGGATGACAGATGCATTCTGCATTGTGCAAACTTTAA
TGTTTTATTCTCTACAGTGTTCCCACTTACAAGTTTTGGACCACTAGTGAGAAAAATATTTGTTGATGGT
GTTCCATTTGTAGTTTCAACTGGATACCACTTCAGAGAGCTAGGTGTTGTACATAATCAGGATGTAAACT
TACATAGCTCTAGACTTAGTTTTAAGGAATTACTTGTGTATGCTGCTGACCCTGCTATGCACGCTGCTTC
TGGTAATCTATTACTAGATAAACGCACTACGTGCTTTTCAGTAGCTGCACTTACTAACAATGTTGCTTTT
CAAACTGTCAAACCCGGTAATTTTAACAAAGACTTCTATGACTTTGCTGTGTCTAAGGGTTTCTTTAAGG
AAGGAAGTTCTGTTGAATTAAAACACTTCTTCTTTGCTCAGGATGGTAATGCTGCTATCAGCGATTATGA
CTACTATCGTTATAATCTACCAACAATGTGTGATATCAGACAACTACTATTTGTAGTTGAAGTTGTTGAT
AAGTACTTTGATTGTTACGATGGTGGCTGTATTAATGCTAACCAAGTCATCGTCAACAACCTAGACAAAT
CAGCTGGTTTTCCATTTAATAAATGGGGTAAGGCTAGACTTTATTATGATTCAATGAGTTATGAGGATCA
AGATGCACTTTTCGCATATACAAAACGTAATGTCATCCCTACTATAACTCAAATGAATCTTAAGTATGCC
ATTAGTGCAAAGAATAGAGCTCGCACCGTAGCTGGTGTCTCTATCTGTAGTACTATGACCAATAGACAGT
TTCATCAAAAATTATTGAAATCAATAGCCGCCACTAGAGGAGCTACTGTAGTAATTGGAACAAGCAAATT
CTATGGTGGTTGGCACAACATGTTAAAAACTGTTTATAGTGATGTAGAAAACCCTCACCTTATGGGTTGG
GATTATCCTAAATGTGATAGAGCCATGCCTAACATGCTTAGAATTATGGCCTCACTTGTTCTTGCTCGCA
AACATACAACGTGTTGTAGCTTGTCACACCGTTTCTATAGATTAGCTAATGAGTGTGCTCAAGTATTGAG
TGAAATGGTCATGTGTGGCGGTTCACTATATGTTAAACCAGGTGGAACCTCATCAGGAGATGCCACAACT
GCTTATGCTAATAGTGTTTTTAACATTTGTCAAGCTGTCACGGCCAATGTTAATGCACTTTTATCTACTG
ATGGTAACAAAATTGCCGATAAGTATGTCCGCAATTTACAACACAGACTTTATGAGTGTCTCTATAGAAA
TAGAGATGTTGACACAGACTTTGTGAATGAGTTTTACGCATATTTGCGTAAACATTTCTCAATGATGATA
CTCTCTGACGATGCTGTTGTGTGTTTCAATAGCACTTATGCATCTCAAGGTCTAGTGGCTAGCATAAAGA
ACTTTAAGTCAGTTCTTTATTATCAAAACAATGTTTTTATGTCTGAAGCAAAATGTTGGACTGAGACTGA
CCTTACTAAAGGACCTCATGAATTTTGCTCTCAACATACAATGCTAGTTAAACAGGGTGATGATTATGTG
TACCTTCCTTACCCAGATCCATCAAGAATCCTAGGGGCCGGCTGTTTTGTAGATGATATCGTAAAAACAG
ATGGTACACTTATGATTGAACGGTTCGTGTCTTTAGCTATAGATGCTTACCCACTTACTAAACATCCTAA
TCAGGAGTATGCTGATGTCTTTCATTTGTACTTACAATACATAAGAAAGCTACATGATGAGTTAACAGGA
CACATGTTAGACATGTATTCTGTTATGCTTACTAATGATAACACTTCAAGGTATTGGGAACCTGAGTTTT
ATGAGGCTATGTACACACCGCATACAGTCTTACAGGCTGTTGGGGCTTGTGTTCTTTGCAATTCACAGAC
TTCATTAAGATGTGGTGCTTGCATACGTAGACCATTCTTATGTTGTAAATGCTGTTACGACCATGTCATA
TCAACATCACATAAATTAGTCTTGTCTGTTAATCCGTATGTTTGCAATGCTCCAGGTTGTGATGTCACAG
ATGTGACTCAACTTTACTTAGGAGGTATGAGCTATTATTGTAAATCACATAAACCACCCATTAGTTTTCC
ATTGTGTGCTAATGGACAAGTTTTTGGTTTATATAAAAATACATGTGTTGGTAGCGATAATGTTACTGAC
TTTAATGCAATTGCAACATGTGACTGGACAAATGCTGGTGATTACATTTTAGCTAACACCTGTACTGAAA
GACTCAAGCTTTTTGCAGCAGAAACGCTCAAAGCTACTGAGGAGACATTTAAACTGTCTTATGGTATTGC
TACTGTACGTGAAGTGCTGTCTGACAGAGAATTACATCTTTCATGGGAAGTTGGTAAACCTAGACCACCA
CTTAACCGAAATTATGTCTTTACTGGTTATCGTGTAACTAAAAACAGTAAAGTACAAATAGGAGAGTACA
CCTTTGAAAAAGGTGACTATGGTGATGCTGTTGTTTACCGAGGTACAACAACTTACAAATTAAATGTTGG
TGATTATTTTGTGCTGACATCACATACAGTAATGCCATTAAGTGCACCTACACTAGTGCCACAAGAGCAC
TATGTTAGAATTACTGGCTTATACCCAACACTCAATATCTCAGATGAGTTTTCTAGCAATGTTGCAAATT
ATCAAAAGGTTGGTATGCAAAAGTATTCTACACTCCAGGGACCACCTGGTACTGGTAAGAGTCATTTTGC
TATTGGCCTAGCTCTCTACTACCCTTCTGCTCGCATAGTGTATACAGCTTGCTCTCATGCCGCTGTTGAT
GCACTATGTGAGAAGGCATTAAAATATTTGCCTATAGATAAATGTAGTAGAATTATACCTGCACGTGCTC
GTGTAGAGTGTTTTGATAAATTCAAAGTGAATTCAACATTAGAACAGTATGTCTTTTGTACTGTAAATGC
ATTGCCTGAGACGACAGCAGATATAGTTGTCTTTGATGAAATTTCAATGGCCACAAATTATGATTTGAGT
GTTGTCAATGCCAGATTACGTGCTAAGCACTATGTGTACATTGGCGACCCTGCTCAATTACCTGCACCAC
GCACATTGCTAACTAAGGGCACACTAGAACCAGAATATTTCAATTCAGTGTGTAGACTTATGAAAACTAT
AGGTCCAGACATGTTCCTCGGAACTTGTCGGCGTTGTCCTGCTGAAATTGTTGACACTGTGAGTGCTTTG
GTTTATGATAATAAGCTTAAAGCACATAAAGACAAATCAGCTCAATGCTTTAAAATGTTTTATAAGGGTG
TTATCACGCATGATGTTTCATCTGCAATTAACAGGCCACAAATAGGCGTGGTAAGAGAATTCCTTACACG
TAACCCTGCTTGGAGAAAAGCTGTCTTTATTTCACCTTATAATTCACAGAATGCTGTAGCCTCAAAGATT
TTGGGACTACCAACTCAAACTGTTGATTCATCACAGGGCTCAGAATATGACTATGTCATATTCACTCAAA
CCACTGAAACAGCTCACTCTTGTAATGTAAACAGATTTAATGTTGCTATTACCAGAGCAAAAGTAGGCAT
ACTTTGCATAATGTCTGATAGAGACCTTTATGACAAGTTGCAATTTACAAGTCTTGAAATTCCACGTAGG
AATGTGGCAACTTTACAAGCTGAAAATGTAACAGGACTCTTTAAAGATTGTAGTAAGGTAATCACTGGGT
TACATCCTACACAGGCACCTACACACCTCAGTGTTGACACTAAATTCAAAACTGAAGGTTTATGTGTTGA
CATACCTGGCATACCTAAGGACATGACCTATAGAAGACTCATCTCTATGATGGGTTTTAAAATGAATTAT
CAAGTTAATGGTTACCCTAACATGTTTATCACCCGCGAAGAAGCTATAAGACATGTACGTGCATGGATTG
GCTTCGATGTCGAGGGGTGTCATGCTACTAGAGAAGCTGTTGGTACCAATTTACCTTTACAGCTAGGTTT
TTCTACAGGTGTTAACCTAGTTGCTGTACCTACAGGTTATGTTGATACACCTAATAATACAGATTTTTCC
AGAGTTAGTGCTAAACCACCGCCTGGAGATCAATTTAAACACCTCATACCACTTATGTACAAAGGACTTC
CTTGGAATGTAGTGCGTATAAAGATTGTACAAATGTTAAGTGACACACTTAAAAATCTCTCTGACAGAGT
CGTATTTGTCTTATGGGCACATGGCTTTGAGTTGACATCTATGAAGTATTTTGTGAAAATAGGACCTGAG
CGCACCTGTTGTCTATGTGATAGACGTGCCACATGCTTTTCCACTGCTTCAGACACTTATGCCTGTTGGC
ATCATTCTATTGGATTTGATTACGTCTATAATCCGTTTATGATTGATGTTCAACAATGGGGTTTTACAGG
TAACCTACAAAGCAACCATGATCTGTATTGTCAAGTCCATGGTAATGCACATGTAGCTAGTTGTGATGCA
ATCATGACTAGGTGTCTAGCTGTCCACGAGTGCTTTGTTAAGCGTGTTGACTGGACTATTGAATATCCTA
TAATTGGTGATGAACTGAAGATTAATGCGGCTTGTAGAAAGGTTCAACACATGGTTGTTAAAGCTGCATT
ATTAGCAGACAAATTCCCAGTTCTTCACGACATTGGTAACCCTAAAGCTATTAAGTGTGTACCTCAAGCT
GATGTAGAATGGAAGTTCTATGATGCACAGCCTTGTAGTGACAAAGCTTATAAAATAGAAGAATTATTCT
ATTCTTATGCCACACATTCTGACAAATTCACAGATGGTGTATGCCTATTTTGGAATTGCAATGTCGATAG
ATATCCTGCTAATTCCATTGTTTGTAGATTTGACACTAGAGTGCTATCTAACCTTAACTTGCCTGGTTGT
GATGGTGGCAGTTTGTATGTAAATAAACATGCATTCCACACACCAGCTTTTGATAAAAGTGCTTTTGTTA
ATTTAAAACAATTACCATTTTTCTATTACTCTGACAGTCCATGTGAGTCTCATGGAAAACAAGTAGTGTC
AGATATAGATTATGTACCACTAAAGTCTGCTACGTGTATAACACGTTGCAATTTAGGTGGTGCTGTCTGT
AGACATCATGCTAATGAGTACAGATTGTATCTCGATGCTTATAACATGATGATCTCAGCTGGCTTTAGCT
TGTGGGTTTACAAACAATTTGATACTTATAACCTCTGGAACACTTTTACAAGACTTCAGAGTTTAGAAAA
TGTGGCTTTTAATGTTGTAAATAAGGGACACTTTGATGGACAACAGGGTGAAGTACCAGTTTCTATCATT
AATAACACTGTTTACACAAAAGTTGATGGTGTTGATGTAGAATTGTTTGAAAATAAAACAACATTACCTG
TTAATGTAGCATTTGAGCTTTGGGCTAAGCGCAACATTAAACCAGTACCAGAGGTGAAAATACTCAATAA
TTTGGGTGTGGACATTGCTGCTAATACTGTGATCTGGGACTACAAAAGAGATGCTCCAGCACATATATCT
ACTATTGGTGTTTGTTCTATGACTGACATAGCCAAGAAACCAACTGAAACGATTTGTGCACCACTCACTG
TCTTTTTTGATGGTAGAGTTGATGGTCAAGTAGACTTATTTAGAAATGCCCGTAATGGTGTTCTTATTAC
AGAAGGTAGTGTTAAAGGTTTACAACCATCTGTAGGTCCCAAACAAGCTAGTCTTAATGGAGTCACATTA
ATTGGAGAAGCCGTAAAAACACAGTTCAATTATTATAAGAAAGTTGATGGTGTTGTCCAACAATTACCTG
AAACTTACTTTACTCAGAGTAGAAATTTACAAGAATTTAAACCCAGGAGTCAAATGGAAATTGATTTCTT
AGAATTAGCTATGGATGAATTCATTGAACGGTATAAATTAGAAGGCTATGCCTTCGAACATATCGTTTAT
GGAGATTTTAGTCATAGTCAGTTAGGTGGTTTACATCTACTGATTGGACTAGCTAAACGTTTTAAGGAAT
CACCTTTTGAATTAGAAGATTTTATTCCTATGGACAGTACAGTTAAAAACTATTTCATAACAGATGCGCA
AACAGGTTCATCTAAGTGTGTGTGTTCTGTTATTGATTTATTACTTGATGATTTTGTTGAAATAATAAAA
TCCCAAGATTTATCTGTAGTTTCTAAGGTTGTCAAAGTGACTATTGACTATACAGAAATTTCATTTATGC
TTTGGTGTAAAGATGGCCATGTAGAAACATTTTACCCAAAATTACAATCTAGTCAAGCGTGGCAACCGGG
TGTTGCTATGCCTAATCTTTACAAAATGCAAAGAATGCTATTAGAAAAGTGTGACCTTCAAAATTATGGT
GATAGTGCAACATTACCTAAAGGCATAATGATGAATGTCGCAAAATATACTCAACTGTGTCAATATTTAA
ACACATTAACATTAGCTGTACCCTATAATATGAGAGTTATACATTTTGGTGCTGGTTCTGATAAAGGAGT
TGCACCAGGTACAGCTGTTTTAAGACAGTGGTTGCCTACGGGTACGCTGCTTGTCGATTCAGATCTTAAT
GACTTTGTCTCTGATGCAGATTCAACTTTGATTGGTGATTGTGCAACTGTACATACAGCTAATAAATGGG
ATCTCATTATTAGTGATATGTACGACCCTAAGACTAAAAATGTTACAAAAGAAAATGACTCTAAAGAGGG
TTTTTTCACTTACATTTGTGGGTTTATACAACAAAAGCTAGCTCTTGGAGGTTCCGTGGCTATAAAGATA
ACAGAACATTCTTGGAATGCTGATCTTTATAAGCTCATGGGACACTTCGCATGGTGGACAGCCTTTGTTA
CTAATGTGAATGCGTCATCATCTGAAGCATTTTTAATTGGATGTAATTATCTTGGCAAACCACGCGAACA
AATAGATGGTTATGTCATGCATGCAAATTACATATTTTGGAGGAATACAAATCCAATTCAGTTGTCTTCC
TATTCTTTATTTGACATGAGTAAATTTCCCCTTAAATTAAGGGGTACTGCTGTTATGTCTTTAAAAGAAG
GTCAAATCAATGATATGATTTTATCTCTTCTTAGTAAAGGTAGACTTATAATTAGAGAAAACAACAGAGT
TGTTATTTCTAGTGATGTTCTTGTTAACAACTAAACGAACAATGTTTGTTTTTCTTGTTTTATTGCCACT
AGTCTCTAGTCAGTGTGTTAATCTTACAACCAGAACTCAATTACCCCCTGCATACACTAATTCTTTCACA
CGTGGTGTTTATTACCCTGACAAAGTTTTCAGATCCTCAGTTTTACATTCAACTCAGGACTTGTTCTTAC
CTTTCTTTTCCAATGTTACTTGGTTCCATGCTATACATGTCTCTGGGACCAATGGTACTAAGAGGTTTGA
TAACCCTGTCCTACCATTTAATGATGGTGTTTATTTTGCTTCCACTGAGAAGTCTAACATAATAAGAGGC
TGGATTTTTGGTACTACTTTAGATTCGAAGACCCAGTCCCTACTTATTGTTAATAACGCTACTAATGTTG
TTATTAAAGTCTGTGAATTTCAATTTTGTAATGATCCATTTTTGGGTGTTTATTACCACAAAAACAACAA
AAGTTGGATGGAAAGTGAGTTCAGAGTTTATTCTAGTGCGAATAATTGCACTTTTGAATATGTCTCTCAG
CCTTTTCTTATGGACCTTGAAGGAAAACAGGGTAATTTCAAAAATCTTAGGGAATTTGTGTTTAAGAATA
TTGATGGTTATTTTAAAATATATTCTAAGCACACGCCTATTAATTTAGTGCGTGATCTCCCTCAGGGTTT
TTCGGCTTTAGAACCATTGGTAGATTTGCCAATAGGTATTAACATCACTAGGTTTCAAACTTTACTTGCT
TTACATAGAAGTTATTTGACTCCTGGTGATTCTTCTTCAGGTTGGACAGCTGGTGCTGCAGCTTATTATG
TGGGTTATCTTCAACCTAGGACTTTTCTATTAAAATATAATGAAAATGGAACCATTACAGATGCTGTAGA
CTGTGCACTTGACCCTCTCTCAGAAACAAAGTGTACGTTGAAATCCTTCACTGTAGAAAAAGGAATCTAT
CAAACTTCTAACTTTAGAGTCCAACCAACAGAATCTATTGTTAGATTTCCTAATATTACAAACTTGTGCC
CTTTTGGTGAAGTTTTTAACGCCACCAGATTTGCATCTGTTTATGCTTGGAACAGGAAGAGAATCAGCAA
CTGTGTTGCTGATTATTCTGTCCTATATAATTCCGCATCATTTTCCACTTTTAAGTGTTATGGAGTGTCT
CCTACTAAATTAAATGATCTCTGCTTTACTAATGTCTATGCAGATTCATTTGTAATTAGAGGTGATGAAG
TCAGACAAATCGCTCCAGGGCAAACTGGAAAGATTGCTGATTATAATTATAAATTACCAGATGATTTTAC
AGGCTGCGTTATAGCTTGGAATTCTAACAATCTTGATTCTAAGGTTGGTGGTAATTATAATTACCTGTAT
AGATTGTTTAGGAAGTCTAATCTCAAACCTTTTGAGAGAGATATTTCAACTGAAATCTATCAGGCCGGTA
GCACACCTTGTAATGGTGTTGAAGGTTTTAATTGTTACTTTCCTTTACAATCATATGGTTTCCAACCCAC
TAATGGTGTTGGTTACCAACCATACAGAGTAGTAGTACTTTCTTTTGAACTTCTACATGCACCAGCAACT
GTTTGTGGACCTAAAAAGTCTACTAATTTGGTTAAAAACAAATGTGTCAATTTCAACTTCAATGGTTTAA
CAGGCACAGGTGTTCTTACTGAGTCTAACAAAAAGTTTCTGCCTTTCCAACAATTTGGCAGAGACATTGC
TGACACTACTGATGCTGTCCGTGATCCACAGACACTTGAGATTCTTGACATTACACCATGTTCTTTTGGT
GGTGTCAGTGTTATAACACCAGGAACAAATACTTCTAACCAGGTTGCTGTTCTTTATCAGGGTGTTAACT
GCACAGAAGTCCCTGTTGCTATTCATGCAGATCAACTTACTCCTACTTGGCGTGTTTATTCTACAGGTTC
TAATGTTTTTCAAACACGTGCAGGCTGTTTAATAGGGGCTGAACATGTCAACAACTCATATGAGTGTGAC
ATACCCATTGGTGCAGGTATATGCGCTAGTTATCAGACTCAGACTAATTCTCCTCGGCGGGCACGTAGTG
TAGCTAGTCAATCCATCATTGCCTACACTATGTCACTTGGTGCAGAAAATTCAGTTGCTTACTCTAATAA
CTCTATTGCCATACCCACAAATTTTACTATTAGTGTTACCACAGAAATTCTACCAGTGTCTATGACCAAG
ACATCAGTAGATTGTACAATGTACATTTGTGGTGATTCAACTGAATGCAGCAATCTTTTGTTGCAATATG
GCAGTTTTTGTACACAATTAAACCGTGCTTTAACTGGAATAGCTGTTGAACAAGACAAAAACACCCAAGA
AGTTTTTGCACAAGTCAAACAAATTTACAAAACACCACCAATTAAAGATTTTGGTGGTTTTAATTTTTCA
CAAATATTACCAGATCCATCAAAACCAAGCAAGAGGTCATTTATTGAAGATCTACTTTTCAACAAAGTGA
CACTTGCAGATGCTGGCTTCATCAAACAATATGGTGATTGCCTTGGTGATATTGCTGCTAGAGACCTCAT
TTGTGCACAAAAGTTTAACGGCCTTACTGTTTTGCCACCTTTGCTCACAGATGAAATGATTGCTCAATAC
ACTTCTGCACTGTTAGCGGGTACAATCACTTCTGGTTGGACCTTTGGTGCAGGTGCTGCATTACAAATAC
CATTTGCTATGCAAATGGCTTATAGGTTTAATGGTATTGGAGTTACACAGAATGTTCTCTATGAGAACCA
AAAATTGATTGCCAACCAATTTAATAGTGCTATTGGCAAAATTCAAGACTCACTTTCTTCCACAGCAAGT
GCACTTGGAAAACTTCAAGATGTGGTCAACCAAAATGCACAAGCTTTAAACACGCTTGTTAAACAACTTA
GCTCCAATTTTGGTGCAATTTCAAGTGTTTTAAATGATATCCTTTCACGTCTTGACAAAGTTGAGGCTGA
AGTGCAAATTGATAGGTTGATCACAGGCAGACTTCAAAGTTTGCAGACATATGTGACTCAACAATTAATT
AGAGCTGCAGAAATCAGAGCTTCTGCTAATCTTGCTGCTACTAAAATGTCAGAGTGTGTACTTGGACAAT
CAAAAAGAGTTGATTTTTGTGGAAAGGGCTATCATCTTATGTCCTTCCCTCAGTCAGCACCTCATGGTGT
AGTCTTCTTGCATGTGACTTATGTCCCTGCACAAGAAAAGAACTTCACAACTGCTCCTGCCATTTGTCAT
GATGGAAAAGCACACTTTCCTCGTGAAGGTGTCTTTGTTTCAAATGGCACACACTGGTTTGTAACACAAA
GGAATTTTTATGAACCACAAATCATTACTACAGACAACACATTTGTGTCTGGTAACTGTGATGTTGTAAT
AGGAATTGTCAACAACACAGTTTATGATCCTTTGCAACCTGAATTAGACTCATTCAAGGAGGAGTTAGAT
AAATATTTTAAGAATCATACATCACCAGATGTTGATTTAGGTGACATCTCTGGCATTAATGCTTCAGTTG
TAAACATTCAAAAAGAAATTGACCGCCTCAATGAGGTTGCCAAGAATTTAAATGAATCTCTCATCGATCT
CCAAGAACTTGGAAAGTATGAGCAGTATATAAAATGGCCATGGTACATTTGGCTAGGTTTTATAGCTGGC
TTGATTGCCATAGTAATGGTGACAATTATGCTTTGCTGTATGACCAGTTGCTGTAGTTGTCTCAAGGGCT
GTTGTTCTTGTGGATCCTGCTGCAAATTTGATGAAGACGACTCTGAGCCAGTGCTCAAAGGAGTCAAATT
ACATTACACATAAACGAACTTATGGATTTGTTTATGAGAATCTTCACAATTGGAACTGTAACTTTGAAGC
AAGGTGAAATCAAGGATGCTACTCCTTCAGATTTTGTTCGCGCTACTGCAACGATACCGATACAAGCCTC
ACTCCCTTTCGGATGGCTTATTGTTGGCGTTGCACTTCTTGCTGTTTTTCATAGCGCTTCCAAAATCATA
ACCCTCAAAAAGAGATGGCAACTAGCACTCTCCAAGGGTGTTCACTTTGTTTGCAACTTGCTGTTGTTGT
TTGTAACAGTTTACTCACACCTTTTGCTCGTTGCTGCTGGCCTTGAAGCCCCTTTTCTCTATCTTTATGC
TTTAGTCTACTTCTTGCAGAGTATAAACTTTGTAAGAATAATAATGAGGCTTTGGCTTTGCTGGAAATGC
CGTTCCAAAAACCCATTACTTTATGATGCCAACTATTTTCTTTGCTGGCATACTAATTGTTACGACTATT
GTATACCTTACAATAGTGTAACTTCTTCAATTGTCATTACTTCAGGTGATGGCACAACAAGTCCTATTTC
TGAACATGACTACCAGATTGGTGGTTATACTGAAAAATGGGAATCTGGAGTAAAAGACTGTGTTGTATTA
CACAGTTACTTCACTTCAGACTATTACCAGCTGTACTCAACTCAATTGAGTACAGACACTGGTGTTGAAC
ATGTTACCTTCTTCATCTACAATAAAATTGTTGATGAGCCTGAAGAACATGTCCAAATTCACACAATCGA
CGGTTCATCCGGAGTTGTTAATCCAGTAATGGAACCAATTTATGATGAACCGACGACGACTACTAGCGTG
CCTTTGTAAGCACAAGCTGATTAGTACGAACTTATGTACTCATTCGTTTCGGAAGAGACAGGTACGTTAA
TAGTTAATAGCGTACTTCTTTTTCTTGCTTTCGTGGTATTCTTGCTAGTTACACTAGCCATCCTTACTGC
GCTTCGATTGTGTGCGTACTGCTGCAATATTGTTAACGTGAGTCTTGTAAAACCTTCTTTTTACGTTTAC
TCTCGTGTTAAAAATCTGAATTCTTCTAGAGTTCCTGATCTTCTGGTCTAAACGAACTAAATATTATATT
AGTTTTTCTGTTTGGAACTTTAATTTTAGCCATGGCAGATTCCAACGGTACTATTACCGTTGAAGAGCTT
AAAAAGCTCCTTGAACAATGGAACCTAGTAATAGGTTTCCTATTCCTTACATGGATTTGTCTTCTACAAT
TTGCCTATGCCAACAGGAATAGGTTTTTGTATATAATTAAGTTAATTTTCCTCTGGCTGTTATGGCCAGT
AACTTTAGCTTGTTTTGTGCTTGCTGCTGTTTACAGAATAAATTGGATCACCGGTGGAATTGCTATCGCA
ATGGCTTGTCTTGTAGGCTTGATGTGGCTCAGCTACTTCATTGCTTCTTTCAGACTGTTTGCGCGTACGC
GTTCCATGTGGTCATTCAATCCAGAAACTAACATTCTTCTCAACGTGCCACTCCATGGCACTATTCTGAC
CAGACCGCTTCTAGAAAGTGAACTCGTAATCGGAGCTGTGATCCTTCGTGGACATCTTCGTATTGCTGGA
CACCATCTAGGACGCTGTGACATCAAGGACCTGCCTAAAGAAATCACTGTTGCTACATCACGAACGCTTT
CTTATTACAAATTGGGAGCTTCGCAGCGTGTAGCAGGTGACTCAGGTTTTGCTGCATACAGTCGCTACAG
GATTGGCAACTATAAATTAAACACAGACCATTCCAGTAGCAGTGACAATATTGCTTTGCTTGTACAGTAA
GTGACAACAGATGTTTCATCTCGTTGACTTTCAGGTTACTATAGCAGAGATATTACTAATTATTATGAGG
ACTTTTAAAGTTTCCATTTGGAATCTTGATTACATCATAAACCTCATAATTAAAAATTTATCTAAGTCAC
TAACTGAGAATAAATATTCTCAATTAGATGAAGAGCAACCAATGGAGATTGATTAAACGAACATGAAAAT
TATTCTTTTCTTGGCACTGATAACACTCGCTACTTGTGAGCTTTATCACTACCAAGAGTGTGTTAGAGGT
ACAACAGTACTTTTAAAAGAACCTTGCTCTTCTGGAACATACGAGGGCAATTCACCATTTCATCCTCTAG
CTGATAACAAATTTGCACTGACTTGCTTTAGCACTCAATTTGCTTTTGCTTGTCCTGACGGCGTAAAACA
CGTCTATCAGTTACGTGCCAGATCAGTTTCACCTAAACTGTTCATCAGACAAGAGGAAGTTCAAGAACTT
TACTCTCCAATTTTTCTTATTGTTGCGGCAATAGTGTTTATAACACTTTGCTTCACACTCAAAAGAAAGA
CAGAATGATTGAACTTTCATTAATTGACTTCTATTTGTGCTTTTTAGCCTTTCTGCTATTCCTTGTTTTA
ATTATGCTTATTATCTTTTGGTTCTCACTTGAACTGCAAGATCATAATGAAACTTGTCACGCCTAAACGA
ACATGAAATTTCTTGTTTTCTTAGGAATCATCACAACTGTAGCTGCATTTCACCAAGAATGTAGTTTACA
GTCATGTACTCAACATCAACCATATGTAGTTGATGACCCGTGTCCTATTCACTTCTATTCTAAATGGTAT
ATTAGAGTAGGAGCTAGAAAATCAGCACCTTTAATTGAATTGTGCGTGGATGAGGCTGGTTCTAAATCAC
CCATTCAGTACATCGATATCGGTAATTATACAGTTTCCTGTTTACCTTTTACAATTAATTGCCAGGAACC
TAAATTGGGTAGTCTTGTAGTGCGTTGTTCGTTCTATGAAGACTTTTTAGAGTATCATGACGTTCGTGTT
GTTTTAGATTTCATCTAAACGAACAAACTAAAATGTCTGATAATGGACCCCAAAATCAGCGAAATGCACC
CCGCATTACGTTTGGTGGACCCTCAGATTCAACTGGCAGTAACCAGAATGGAGAACGCAGTGGGGCGCGA
TCAAAACAACGTCGGCCCCAAGGTTTACCCAATAATACTGCGTCTTGGTTCACCGCTCTCACTCAACATG
GCAAGGAAGACCTTAAATTCCCTCGAGGACAAGGCGTTCCAATTAACACCAATAGCAGTCCAGATGACCA
AATTGGCTACTACCGAAGAGCTACCAGACGAATTCGTGGTGGTGACGGTAAAATGAAAGATCTCAGTCCA
AGATGGTATTTCTACTACCTAGGAACTGGGCCAGAAGCTGGACTTCCCTATGGTGCTAACAAAGACGGCA
TCATATGGGTTGCAACTGAGGGAGCCTTGAATACACCAAAAGATCACATTGGCACCCGCAATCCTGCTAA
CAATGCTGCAATCGTGCTACAACTTCCTCAAGGAACAACATTGCCAAAAGGCTTCTACGCAGAAGGGAGC
AGAGGCGGCAGTCAAGCCTCTTCTCGTTCCTCATCACGTAGTCGCAACAGTTCAAGAAATTCAACTCCAG
GCAGCAGTAGGGGAACTTCTCCTGCTAGAATGGCTGGCAATGGCGGTGATGCTGCTCTTGCTTTGCTGCT
GCTTGACAGATTGAACCAGCTTGAGAGCAAAATGTCTGGTAAAGGCCAACAACAACAAGGCCAAACTGTC
ACTAAGAAATCTGCTGCTGAGGCTTCTAAGAAGCCTCGGCAAAAACGTACTGCCACTAAAGCATACAATG
TAACACAAGCTTTCGGCAGACGTGGTCCAGAACAAACCCAAGGAAATTTTGGGGACCAGGAACTAATCAG
ACAAGGAACTGATTACAAACATTGGCCGCAAATTGCACAATTTGCCCCCAGCGCTTCAGCGTTCTTCGGA
ATGTCGCGCATTGGCATGGAAGTCACACCTTCGGGAACGTGGTTGACCTACACAGGTGCCATCAAATTGG
ATGACAAAGATCCAAATTTCAAAGATCAAGTCATTTTGCTGAATAAGCATATTGACGCATACAAAACATT
CCCACCAACAGAGCCTAAAAAGGACAAAAAGAAGAAGGCTGATGAAACTCAAGCCTTACCGCAGAGACAG
AAGAAACAGCAAACTGTGACTCTTCTTCCTGCTGCAGATTTGGATGATTTCTCCAAACAATTGCAACAAT
CCATGAGCAGTGCTGACTCAACTCAGGCCTAAACTCATGCAGACCACACAAGGCAGATGGGCTATATAAA
CGTTTTCGCTTTTCCGTTTACGATATATAGTCTACTCTTGTGCAGAATGAATTCTCGTAACTACATAGCA
CAAGTAGATGTAGTTAACTTTAATCTCACATAGCAATCTTTAATCAGTGTGTAACATTAGGGAGGACTTG
AAAGAGCCACCACATTTTCACCGAGGCCACGCGGAGTACGATCGAGTGTACAGTGAACAATGCTAGGGAG
AGCTGCCTATATGGAAGAGCCCTAATGTGTAAAATTAATTTTAGTAGTGCTATCCCCATGTGATTTTAAT
AGCTTCTTAGGAGAATGACAANNAAAAAAAAAA

This is the complete nucleotide sequence of a sample of the SARS-CoV-2 virus taken here in Illinois on March 13, 2020. Source is the National Center for Biotechnology Information, GenBank sequence record MT263433.1.

This is just one of 3,863 samples of the SARS-CoV-2 virus in the April 15, 2020 GenBank release. Laboratories use these sequences to make tests, epidemiologists are using them to track the spread of the virus, and vaccine makers have used them to design candidate vaccines.

I suppose if we’ve got to suffer from a world-wide fatal respiratory virus epidemic, this kind of technology makes this the best time in history for it.

(Actually, I guess ancient historic times and recent prehistoric eras might have been better, because this epidemic wouldn’t have gotten very far without cities or travel between them. But we would have had other problems.)

This post by Mark Draughn at Windypundit was originally published at Portrait of the enemy

This post is basically just my way of thinking out loud about the epidemic. For rather a lot of words. Consider yourself warned.

There’s a funny series of animated videos called How It Should Have Ended, that suggests “better” endings for movies, many of which would have ended the movies a lot sooner. (E.g. Make sure the maintenance doors to the dinosaur pens are too small for dinosaurs to escape.) Well, there’s a way we could have ended the Covid-19 epidemic in the United States a lot sooner.

When the first Covid-19 outbreaks were detected, what we should have done is isolate those people, identify everyone they had come in contact with, tracked them down and tested them, isolated the ones who tested positive, then repeated the process for they had contact with, and so on, until the tracing teams identified and isolated everyone who could possibly spread the disease. Doing this for every outbreak would have stopped Covid-19 in its tracks. Contagious diseases all over the world have been beaten this way.

And we did try to do that. Unfortunately, for various reasons (which should be thoroughly investigated by Congress at some point) there weren’t enough tests available and the process broke down. Soon hospitals — some of which resorted out of expediency to tests that were not FDA-approved — began discovering Covid-19 patients who could not be traced back to any other known cluster of Covid-19 cases. This is called community transmission, and it means that the effort to contain the contagion has failed, and tracking of individual transmission incidents is no longer feasible. The disease had escaped and was going to burn through the population.

That’s where we are now, with Covid-19 now confirmed to have infected over 1.3 million Americans.

To explain what happens next, I’d like to go back to something I skimmed over in my earlier post about a STAT magazine article that mentioned a Covid-19 model by Dandekar and Barbastathis at MIT. It was a compartmental model — in particular, it’s an SIR model — and I’d like to talk about how that model works.

Like all models, compartmental models are simplifications, and the SIR model I’m going to be talking about is nowhere near sophisticated enough to model an actual epidemic. It’s just a tool for thinking about how epidemics work, and I think it will be useful for understanding the past and future of the Covid-19 epidemic.

Compartmental models split the population into compartments and specify mathematical formulas that describe how people move between the compartments. (If you have a computing background like me, you can think of these as states.) The SIR model defines three compartments:

• Susceptible: The pool of people who could catch the disease.
• Infected: The pool of people who currently have the disease.
• Recovered: The pool of people who have recovered and are now immune.

People move through the compartments, starting as susceptible, becoming infected, and then recovering:

Susceptible –> Infected –> Recovered

Compartmental models include a set of equations that describe how the number of people in each component changes as the model progresses. For our purposes, I’m going to show you a very simple set of equations from the Wikipedia page on epidemic modeling.

Don’t worry, you don’t have to follow the math. (This is, honestly, at the limits of my memory of differential equations class, which I now regret skimming my way through.) The description that follows will explain the model in plain English (I hope).

To run the model, you specify a few parameters (shown here by the greek letters beta and gamma) which we don’t have to worry about, and you set the starting population numbers S and I to the number of people who are Susceptible and Infected, respectively. If we were to set I to zero, indicating that no one is infected, then all of the derivatives will collapse to zero and nothing will change, which is what you’d expect when no one has the disease. Things don’t get started until someone gets infected. Similarly, if we set S to zero, then there’s no one left to catch the disease, and all that happens is that the infected people in I recover to R.

So in order for something useful to happen, we need people with the disease, and people who can catch it, and as the presence of the term SI implies, the rate at which the infection spreads is proportional to both the number of Infected people and the number of Susceptible people. This captures the common-sense notion that the disease is more likely to spread when a lot of Infected people meet a lot of Susceptible people.

In a typical modeling run, we start with almost everyone in the Susceptible compartment, except for a few Infected people who bring the disease into the population. Each Infected person is assumed to transmit the disease to Susceptible people with some probability, which causes the Susceptible people to move to the Infected compartment.

At the beginning of the epidemic, with the number of Infected people so low, any increase in the size of the Infected compartment produces a proportional increase in the rate at which Susceptible people become Infected, so with even more Infected people, the epidemic spreads even faster, feeding on itself in a period of explosive expansion. This is called exponential growth, and it has some scary implications.

The rate at which each infected person infects other people is denoted by the reproduction number R₀. If R₀ =2, for example, then each Infected person can infect two Susceptible people, and each of those new Infected people can infect two more Susceptible people, and so on. If we assume people are infectious for an average of one week, a single infected person can lead to a pandemic that infects everyone on Earth in 33 weeks. It’s a real doomsday scenario.

(Note: I’m using figures like R₀ =2 and a period of 1 week to keep this example simple. These are not based on actual figures for Covid-19.)

Fortunately, the doomsday scenario is not a realistic scenario, because in order for an Infected person to transmit the disease to a Susceptible person, they have to encounter a Susceptible person, but as Susceptible people are infected, they move to the Infected compartment, and the Susceptible compartment shrinks, reducing the probability that each Infected person can infect a Susceptible person. This makes it less and less likely that Infected people will transmit the disease to Susceptible people, effectively reducing the reproduction number R₀ to some lower effective reproduction number R_e.

Initially, a disease might have R_e = R₀ = 2, meaning each Infected person would transmit the disease to two Susceptible people, and so on, for a period that resembles exponential growth. However, when 10% of the population has been Infected (or Recovered), that means 10% of those disease transmissions are wasted on people who cannot be infected, effectively lowering R_e by 10% to 1.8, so that each infected person can only infect 1.8 other people per week. The more the Susceptible pool shrinks, the lower R_e gets, and slower the rate of new infections grows.

Eventually, as the pool of Susceptible people gets small enough, R_e will fall below 1, meaning that Infected people are no longer guaranteed to replace themselves before they transition to the Recovered compartment. The rate of infection stops increasing — i.e. it reaches its peak — and then begins to decrease as the pool of Susceptible people dwindles further. At some point, the shrinkage of the Susceptible pool causes the epidemic to slow down so much that all the Infected people recover recover before any new Susceptible person is infected, letting I reach 0, which means that everything stops changing, and the epidemic ends.

(You may be wondering where people who die fit into this model. To keep things simple, they are usually lumped in with Recovered people since, like Recovered people, they can neither be infected nor infect someone else. That’s why the equations above have no R terms on the right-hand side — the Recovered people have no direct effect on the dynamics of the epidemic. Because of this, some descriptions of the SIR model refer to the R group as Removed instead of Recovered.)

Graphically, the timeline for this scenario in a typical SIR model would look something like this (with Susceptible people in blue, Infected people in red, and Recovered people in green):

(The numbers on the graph are illustrative only, and have no relationship to the numbers in the description above or to the actual Covid-19 epidemic.)

If that seems too simple, you’re right. There are many variations on compartmental models that take into account complicating factors such as delays between infection and contagiousness, reinfections, births, deaths by other causes, multiple groups of people, migrations, interventions, and so on. The flexibility of the compartmental model framework is one of the things that make these models so useful.

One of the goals of our current policy is to “flatten the curve” by implementing a “lockdown” — using social distancing, masks, shutdowns of many businesses, cancellations of large gatherings, and so on. This should reduce R₀, thus reducing the rate at which Susceptible people enter the Infected compartment, without reducing the rate at which Infected people move to the Recovered compartment, thus reducing the number of people in the Infected compartment at any one time. This, in turn, prevents the epidemic from overwhelming the hospital system, as happened in Lombardy, Italy. Flattening the curve might look something like this:

Basically, the reduced R₀ causes the whole process to slow down and take longer, which reduces the height of the Infected peak. (The height of the peak shown here is unrealistically high — over 40% — especially for a large population like the U.S., and is for illustration purposes only.)

Under the right conditions, the natural R₀ of a disease may be low enough that the reduction in the size of the Susceptible pool slows down the spread of the infection so much that all the people in the Infected pool recover before the entire Susceptible group is infected. That produces a result that looks like this, where the infection is over even though almost 20% of the population is still Susceptible.

That’s because under the modeling parameters that I used for this graph, R₀ is so low that when the Susceptible pool is smaller than about 20%, R_e is forced low enough below 1 to eliminate the infection.

This is sometimes referred to as herd immunity, because even though individual people in the Susceptible compartment can still catch the disease if exposed, they are unlikely to be exposed because even if some new Infected people are re-introduced to the population — e.g. travelers from a region where the infection is still active — the same factors that stopped the first outbreak will quickly eliminate the new outbreak as well. Thus while some individuals are susceptible to the infectious disease, the collective population — the herd — is effectively immune.

Some people argue that our best strategy for dealing with the Covid-19 epidemic is to lift the lockdown and let the virus spread until we reach herd immunity, which they estimate might happen when the Susceptible population drops to about 30%. They argue that (1) the economic cost of the lockdown is too high to remain locked down for very long, and (2) unless we are willing to remain locked down for the one or more years it will take to get a vaccine, we will all get infected to the point of herd immunity anyway, so we might as well do it quickly to minimize the economic pain.

I believe this is misguided for several reasons:

• Covid-19 has a non-trivial fatality rate, and allowing 70% of Americans to be infected by it will result in a large number of deaths.
• Even when it doesn’t kill, Covid-19 is a hard disease, and many people will suffer from it. We are learning that some Covid-19 patients develop life-long disabilities.
• Flattening the curve reduces the risk of overwhelming our healthcare capacity, thus increasing the cost in lives and suffering.
• Slowing the spread of the disease gives our healthcare industry more time to learn about the disease, more time to find innovative solutions, and more time to prepare a response, thus reducing the harm from the disease.

I can’t let this go without mentioning that some loathsome people are making the argument that previous generations — World War II veterans, the Greatest Generation — were bravely willing to make the ultimate sacrifice to preserve our way of life, and therefore we should be equally brave and willing to sacrifice…the lives of other people, who we will let die from Covid-19, to preserve our economy. And anyone who refuses to do this is a coward who spits on his ancestors’ memory. (I exaggerate only slightly.)

Seriously, just how messed up do you have to be to think that making economic sacrifices to save American lives is the cowardly move here? If these people really want to show they are bravely willing to help Americans, they should volunteer to be deliberately infected with the SARS-Cov-2 virus to speed up vaccine trials.

Note that I am not dismissing any arguments about “opening up” the economy as sacrificing lives for money. For one thing, it’s better described as risking lives for economic well-being. That is, doing something to improve the quality of life, at the risk of loss of life. People have been making high-stakes decisions like that throughout history — from refugees crossing dangerous waters, to people working at hazardous jobs because they pay well, to consumers who buy smaller cars to save the money for something else. I regard making these kinds of decisions about our own lives as a fundamental right.

Economist Steven E. Landsburg illustrated this concept by asking a question something like “Would you press a button that would prevent a billion migraine headaches if it also killed one person?” He answered that he would, because one life is a small price to pay to prevent so much suffering. That shocked me the first time I read it — he can’t be serious, can he?

But then I thought about it a little and came up with a different way to ask almost the same question: You’ve got a migraine headache, and there’s a new pill on the market that will stop it in 15 minutes. Would you take that pill if there was a 1-in-a-billion chance it would kill you? I’m pretty sure a lot of people would, just as many people take dangerous jobs to make more money. And if people are demonstrably willing to risk the length of their lives to improve the quality of their lives, then there’s an argument to be made that public policy should reflect their choices and try to reach a similar balance between those goals.

However, there are three points I think are important:

• There’s an ugly history of public policy that is far too cautious, adding great cost and inconvenience for little benefit.
• There’s an even uglier history of public policy that regards human lives as disposable.
• The best public policy lets people make their own decisions about their own lives.

Nevertheless, while agreeing in principle that a poor economy also costs lives and causes suffering, I haven’t seen compelling calculations that convince me we’re committing “economic suicide.”

And there is a better way, which I alluded to earlier, and will get back to in a moment.

There’s no denying that much of the current “lockdown” was hurried and poorly planned, with rules that seem wildly inconsistent, and that are too strict in some ways, preventing people and businesses from coming up with flexible responses. That’s always a potential problem with laws and regulations, but the hurried nature of the emergency makes it worse, and the stakes are even higher than normal.

There’s also no denying that a lot of Americans are in financial trouble right now, especially since the lockdown period is dragging on much longer than many people expected. We’ve all seen the protests, and while the assholes get all the attention, there are a lot of people who are simply desperate for the lockdown to end.

The problem is, the lockdown is really more of a “hunker down.” Evidence from data sets like centralized restaurant reservation systems, the travel industry, and GPS tracking of mobile phones shows that much of the change in public behavior came independently of government lockdown orders, which means that lifting the lockdown orders may not do much to restore economic activity. Customers just aren’t going to return to businesses they don’t think are safe.

Simply put, to open up the economy, we have to make economic activity safe.

That brings me right back to the SIR model. By taking all these actions — shutting down schools and businesses, social distancing, wearing masks, washing our hands — we are trying to reduce the probability of transmission of the Covid-19 virus, which will reduce the base reproduction number R₀ of the virus. If we can get R₀ to be less than 1, then the effective reproduction number R_e also has to be less than 1, which will make the epidemic die out. It should cause the Infected compartment to follow that familiar curve we’ve been seeing everywhere:

With 25,000 new cases per day in the U.S. right now, suppressing the curve this way may seem unrealistic. But it’s completely doable. Here’s proof:

If those other countries can do it, there’s no good reason we can’t. (You can check how the U.S. and other countries are doing at EndCoronavirus.org) Here in the U.S., New York City seems to be making good progress. They’ve been through hell, but it looks like they’re making their way back:

So this is totally possible. But the U.S. still has some work to do:

We seem to be stuck on a gently sloping plateau. I think this is partly because the U.S. is big enough for the epidemic to be running on different timelines in different places, so while New York City is coming down, other parts of the country are still rising. I also think that the recent increase in the availability of testing is responsible for at least some the apparent rise in cases in some parts of the U.S. That is, the cases were always there, they just weren’t being picked up until we had more tests.

Once the number of cases drops a lot closer to zero, many kinds of economic activity will become relatively safe again. However, if we go right back to the way things were at the beginning of the epidemic…we will find ourselves at the beginning of another epidemic. We’ll trigger a second wave, and the economic sacrifices we’ve made to fight the first wave will have been for nothing.

We can’t let that happen.

The solution is a return to Plan A: Test, trace, and isolate. This failed the first time, because we weren’t ready and didn’t have enough tests. On March 1, we were doing fewer than 1000 tests per day. We’re now up to over 300,000 tests per day, and that’s expected to grow as more testing capacity comes online.

I’ve seen several different estimates of the number of tests we’ll need to begin opening up again — among other things, it depends on what you mean by “opening up.” The Rockefeller Foundation’s plan recommended testing about 3 million tests/week to reach the next phase, and the folks at Covid Exit Strategy are tracking a target of 500,000 tests per day. Since both of those are around 1% of the U.S. population, I’ve been tracking that as my target. (Shown by the dashed green line above.)

Testing 1% of the U.S. population per week may not sound like much — it would take almost two years to test the entire population. But we don’t need to test the entire population to begin making some safe changes. At that level of testing — assuming the epidemic curves down according to plan — we should have enough testing capacity for hospitals to diagnose patients with respiratory illnesses (which until recently accounted for most testing) while still making tests available to community medical providers and allowing us to effectively screen key personnel, such as hospital staff and transit workers.

With low infection rates, that level of testing should also allow us to have contact tracing teams investigate new Covid-19 cases, find out who the infected person has been in contact with, and get everybody tested. Infected individuals can then be quarantined, ideally in special-purpose isolation facilities, rather than at home where there’s a chance they’ll infect members of their family.

In terms of the SIR model, isolation of people who test positive is the equivalent of creating a model with only a single person, who happens to be in the Infected compartment. Without any Susceptible people around, the only allowed transition is for the Infected person to move to the Recovered compartment (or Removed, if they die). No one else gets infected.

South Korea did a terrific job of test-and-trace when Covid-19 first hit. Despite discovering their first infections at the same time the U.S. did, they’ve only had 11,000 cases and 260 deaths in a population of 50 million. They’ve begun opening up, but they just had a setback when some guy visited a bunch of nightclubs and then tested positive for Covid-19. South Korean health authorities have closed all the clubs, and tested 2400 of the 5500 people who were potentially exposed, identifying 80 cases so far, including 35 in a single day, which is the highest single-day number of new Covid-19 cases in South Korea in the last month.

Imagine how great it would be in the United States if 35 cases in a single day was big news.

Fortunately, opening up the economy and maintaining good infection control aren’t entirely mutually exclusive. There are certainly some activities that will be difficult to do safely, especially those involving close contact or large numbers of people, but I think we can make many things safer with a little ingenuity.

We mostly know what it takes to stop infections from spreading — masks, gloves, gowns, washing hands, cleaning surfaces — and we already have a lot of the basic technology in our healthcare industry. It’s true that a lot of healthcare workers have caught the virus, but given that they are spending so much time in close proximity to people who very definitely have Covid-19, it’s not as many as you might think. There’s even some evidence that infection rates are lower in some healthcare workers than in the general public they serve.

If nurses can figure out how to safely take vitals and draw blood from Covid-19 patients, we can probably figure out protocols to safely cut someone’s hair or sell them retail goods. This will require a massive increase in production of personal protective equipment (PPE), but that’s happening anyway, and healthcare workers won’t need so much of it if we can keep the epidemic small.

We’ll also probably need to develop PPE that is specific to our purposes. Doctors and nurses need to switch out their PPE every time they switch patients, to avoid spreading infections. But in the relatively low-risk environment the rest of us face, that is less likely to be a concern. We might do better with PPE designed for easier fit, comfort, and long-term wear, perhaps even with the possibility of sterilization and cleaning.

It won’t be perfect, but it doesn’t need to be. Anything that helps reduce the probability of transmission can help keep R₀ down.

It’s possible that we will never entirely defeat Covid-19. There are ancient killers still among us, like leprosy, mentioned in the bible, or tuberculosis, which has left signs of infection in the fossilized remains of people who died half a million years ago. Leprosy is largely survivable these days, but tuberculosis still kills about 1.5 million people a year.

We’ve had some successes at eradicating diseases. Smallpox has been wiped out for decades, and two of the three known strains of polio have been eradicated, with the remaining strain thought likely to disappear as well. Malaria has been wiped out in much of the developed world, and may be eradicated from a few remaining stronghold regions in another couple of decades.

Some diseases hide in animal hosts. Ebola has been eliminated from the human population multiple times, only to spring up again when a human somewhere catches a case from whichever animal species is serving as a reservoir. (Bats are a key suspect.) Rabies circulates in mammal populations, and is transferred to humans by a bite, but human-to-human transmission is all but non-existent.

On the other hand, influenza viruses have survived all attempts to eradicate them from the human population. The flu is a modern disease, successful at persisting in the human population because we insist on living close together in giant cities. And it mutates quickly enough that even our vaccines cannot keep up with the changes. The Spanish flu may be gone, but its related H1N1 family of viruses is still killing people.

Fortunately, many of the diseases that survive in the human population have evolved into milder forms. Diseases that kill quickly don’t leave themselves much time to spread, so mutations that leave their hosts alive and mobile are more likely to survive and thrive. We all catch one or another of the 160 identified rhinoviruses several times a year, and we treat them with over-the-counter cold medicine.

Unfortunately, even viruses don’t evolve quickly enough for this to help us right now.

Fortunately, there may be a magic bullet: A vaccine. Last I heard, over 90 labs are trying to develop a vaccine, and 9 of them have begun Phase 1 trials for safety. We’ve never developed a vaccine for a coronavirus in humans before, but we have several for livestock, and experts expect we will be able to make one for SARS-CoV-2 as well. The 12-18 month figure that everyone throws around would probably be the earliest, and it may be optimistic — most vaccines take longer.

When we got hit with the first SARS virus at the beginning of the century, a program was launched to develop a vaccine, but SARS was less contagious than SARS-CoV-2, and it was eliminated in 2004 through the kinds of social distancing and testing measures I outlined above. At that point, vaccine development was abandoned, but scientists learned a thing or two about how to make a vaccine for this type of virus. Also, we’ve gotten super-good at genetic tinkering these days.

In terms of the SIR model, a vaccine works by conferring immunity to a disease on people who’ve never had it, effectively moving people from the Susceptible compartment to Recovered, without ever having to go through the Infected state. This lowers R_e, ideally well below 1, resulting in herd immunity without the need for people to catch the disease or die.

So, that’s the plan: (1) Hunker down now to suppress the outbreak to manageable levels, (2) limit the spread with infection control measures, (3) manage the outbreak with testing, tracing, and isolation, and (4) develop a vaccine.

I hope we’re smart enough, industrious enough, and good enough to make it work.

This post by Mark Draughn at Windypundit was originally published at How the epidemic ends

A widely followed model for projecting Covid-19 deaths in the U.S. is producing results that have been bouncing up and down like an unpredictable fever, and now epidemiologists are criticizing it as flawed and misleading for both the public and policy makers. In particular, they warn against relying on it as the basis for government decision-making, including on “re-opening America.”

Unlike some of the nuttier tweets I quoted in my previous post, these criticisms come from the epidemiological community.

“It’s not a model that most of us in the infectious disease epidemiology field think is well suited” to projecting Covid-19 deaths, epidemiologist Marc Lipsitch of the Harvard T.H. Chan School of Public Health told reporters this week, referring to projections by the Institute for Health Metrics and Evaluation at the University of Washington.

I don’t want to fall into the fallacy of appeal to authority, but since most of us are not expert enough to understand the subject completely ourselves, authority certainly helps make the criticisms more credible. But there are other reasons to take the criticisms in the STAT article seriously.

Credible scientific criticism tends to have certain recognizable characteristics. Most importantly, in order to credibly criticize a piece of science, you have to actually understand the science. The great scientific revolutionaries, such as Albert Einstein, thoroughly understood the system they were seeking to overthrow. Failing to meet this obligation is a common problem with cranks and people driven by ulterior motives.

For example, when the Milken Institute School of Public Health came out with their 2018 study estimating that hurricane María caused 3000 deaths in Puerto Rico, many Trump opponents said it proved the Trump administration’s relief effort was shoddy and ineffective. Some of Trump’s supporters responded with ill-informed attacks on the study, several of which I described in my post on the subject at the time. But what neither side seemed to realize is that the study did not make any claims about the effectiveness of the Trump Administration’s relief effort. It wasn’t designed for that purpose and didn’t have access to the kind of data needed to assess the relief effort. The authors made this clear in their report. Obviously, most of the loud mouths on either side hadn’t actually read and understood how the study worked or what it was intended to discover.

That last part is important. In the absence of clear errors in the science, math, or data wrangling, most studies have a certain basic level of internal correctness. The real question is whether the methodology and data are suitable for the purpose for which the results are used.

Some years ago, the FBI reported statistics showing that most murder victims are killed by people they know. Advocates of stricter gun control leaped on this finding to argue that having a gun in your home would make you more likely to kill a family member than a criminal. But if you looked at how the FBI assembled the data, they included instances of criminals and gang members killing each other as crimes where the victims were killed by people they know. Because of this, the FBI report wasn’t very useful for answering questions about the advisability of having a gun in the home.

(I’m not sure, but I think the FBI was gathering this data because common murder investigation techniques often assumed a connection between victim and perpetrator, but police departments were seeing an increase in murders by strangers, such as serial killers, which required a different approach.)

This can be difficult to get right, and as with most things, the accuracy of understanding of scientific information tends to drop off as we get further and further from the source, and in the worst case can get pretty bad.

• The scientists who actually performed the study usually have a good grasp of its limitations.
• The big-shot scientist whose name is first on the paper might overstate the importance a bit.
• The university or corporate press release will probably get the basic idea right, but they’ll overstate the importance of the result and ignore the nuances and limitations.
• The press will focus on the most sensational aspects of the press release.
• Pundits and politicians will use the press accounts to support their prior beliefs and policies.
• Fringe bloggers and tweeters and political hacks on social media will take the resulting nonsense and pile more nonsense on top.

It doesn’t have to be like that, of course. At any step along they way, the people involved could go back and carefully read the original study paper, thus undoing much of the damage of this scientific game of telephone. (It’s what I try to do. Or failing that, I try to read accounts in the scientific press by reporters who have read the original material and can put it in a context I can understand.) Unfortunately, by the time the careful reading gets out, the crazy has been around the world.

The STAT article links to an article in the Annals of Internal Medicine which argues that the IHME model is not useful for planning:

The IHME projections are based not on transmission dynamics but on a statistical model with no epidemiologic basis. Specifically, the model used reported worldwide COVID-19 deaths and extrapolated similar patterns in mortality growth curves to forecast expected deaths. The technique uses mortality data, which are generally more reliable than testing-dependent confirmed case counts. Outputs suggest precise estimates (albeit with uncertainty bounds) for all regions until the epidemic ends. This appearance of certainty is seductive when the world is desperate to know what lies ahead. However, the underlying data and statistical model must be interpreted cautiously. Here, we raise concerns about the validity and usefulness of the projections for policymakers.

In just that single paragraph, the authors demonstrate that they understand how the IHME model works, and they argue that the model has little to offer for creating policy. The AIM article goes on to list six major areas of concern with the model. I’m not going to quote them — you can read the whole thing if you’re interested — but the article makes a lot of observations about the model in a relatively small space.

That brings me to another point: Credible criticism of science involves discussion of the actual science. For example, the issue of experimenter bias is obviously important, and studies by scientists with a history of bias or conflicts of interest should certainly be scrutinized carefully. However, it drives me nuts when pundits attack scientific studies by making ad hominem accusations of “bias” against the authors — because they’re paid by big oil, or because they donated money to the Clintons, or whatever — without backing it up with evidence from the study.

If you think a scientist is biased or has a conflict of interest, that’s definitely a fair thing to bring up when they’re expressing an opinion as an expert. But if you’re criticizing a scientific study (or experiment or model), you have to do better than that. If your argument is that the scientist’s bias has influenced the outcome of the study, then you should be able to point to the bias in the study. Proper scientific studies are reported out in the open, with detailed descriptions of their methodology, data, and analysis. If you think the scientists mucked it up, you should be able to point out where they made their mistakes.

This isn’t a hard thing to do if you’re familiar with the science. In a study performed by surveying people, you could criticize the choice of community from which subjects were drawn, or of how members are chosen from the community — using voting records, driver’s licenses, or commercial address lists will select for different kinds of people. You can argue that the people who agree to take part in the study are not representative — e.g. people willing to answer a stranger’s questions about their sex lives may be more likely to have unusual sex lives. You could argue that the survey questions have been misinterpreted by the subjects, or that the answers were misinterpreted by the scientists. You could argue that the wrong data sets were used, or that the data was mis-coded by the observers. If the study involves subjective judgement — e.g. doctor’s assessments of patient health — then you could argue that their judgment was influenced by their prior beliefs about the subject under study. The list of possibilities goes on and on, including lots of “gotcha” problems that are specific to a particular type of science. Many scientific studies talk about these issues openly in the interest of full disclosure.

I’m not saying you need have to have iron clad proof of a mistake or misrepresentation to establish bias, but if you are arguing that a scientific study is are biased, then you should be able to identify specific choices that you believe the scientists made because they were biased. That is, if you say the study is wrong (because of bias or any other reason), then you should be able to point out the part that is wrong. This is not a lot to ask.

(Of course, this isn’t always possible with every study. In the worst case, some papers are just poorly written, and you can’t critique how the study was done because the scientists didn’t describe it well enough, or it depends on data that is unavailable. This may prevent you from pointing to the part that is wrong, but it’s also a fair criticism to point out that the study is hard to evaluate, or that its conclusions are poorly supported.)

The authors of the AIM paper aren’t making accusations of bias, but they do specifically identify parts of the model they believe to be incorrect. They are specific about the science, the methodology, and the applicability of the model.

Others experts, including some colleagues of the model-makers, are even harsher. “That the IHME model keeps changing is evidence of its lack of reliability as a predictive tool,” said epidemiologist Ruth Etzioni of the Fred Hutchinson Cancer Center, home to several of the researchers who created the model, and who has served on a search committee for IHME. “That it is being used for policy decisions and its results interpreted wrongly is a travesty unfolding before our eyes.”

Movie director Jean-Luc Godard famously said, “In order to criticize a movie, you have to make another movie.” I don’t think I agree when it comes to movie criticism, but that is how science works. If you think a theory is wrong, pointing out weaknesses will only get you so far, because being wrong is not the same as being useless. As statistician George Box puts it, “All models are wrong, but some are useful.” So the best way to criticize a scientific theory is to offer a more useful theory. And the best way to criticize an epidemic model is to propose a more useful epidemic model.

The STAT article suggests two models that are arguably more useful. The first is a compartmental model from Dandekar and Barbastathis at MIT that takes into account the effects of quarantine measures. Compartmental models split the population into compartments representing different states of the disease for a person — e.g. Susceptible, Infected, and Recovered — and specify equations that describe how people move between the compartments.

The MIT model is grounded in epidemiological principles that have been understood for about a century, and which have been successfully used to predict things like annual influenza in the U.S. It is arguably a better model than the relatively simple IHME model, which just fits numbers to a curve. But is the MIT model accurate?

The model predicted U.S. cases would plateau at about 650,000 cases in mid April, which seemed pretty accurate at the time the STAT article was published. I’ve been lazy in writing this post, however, so I can see that the U.S. is now estimated to have about 860,000 active cases (over a million infected and about 150,000 recovered) as of the end of April, so the model seems to have missed. On the other hand, reporting of recoveries seems to be very delayed, so maybe not by much.

(The second model is a “data-driven” model by Huang, Qiao, and Tung, which sounds like a variation of the approach taken in the IHME model but, to be honest, the methodology goes over my head. I don’t really understand what they’re doing, so I can’t say much about it. This model also seems to have under-predicted the scope of the epidemic, with a mid-April peak and a final total of about 700,000 cases in this wave.)

Regardless of how these other models turned out, the STAT article didn’t just throw shade on the IHME model, it offered alternatives. That’s important because figuring out public health policy for fighting a pandemic is a plan for the future, and as I’ve said before, every time you plan for the future, you are basing your plan on a model. You have some mental idea of how the world works, and how you want to change it. So if you’re going to criticize the current model, you should probably be prepared to offer a better one.

This is why I’m weary of people who make angry claims that the science used to make Covid-19 policy decisions is wrong. Of course it’s wrong. All models are wrong. But that doesn’t mean it isn’t useful. And useful is a relative concept. Even if all you have is poor models, one of them is going to be the most useful model you’ve got.

You think the accepted Covid-19 case fatality rates are wrong? Fair enough, it’s certainly possible, and we can talk about it. But if you’re going to get angry at policy makers for using the accepted numbers, then you need to explain what numbers you think they should be using instead. You may indeed have found a flaw in the model, but if you can’t offer a better model, then you have no right to be angry at people for using the best model they have, at least until a better one comes along.

Addendum:

Here are some resources I found at FiveThirtyEight that might be useful:

• A comic strip explanation of why modeling the Covid-19 epidemic is hard.
• A comparison of 6 prominent Covid-19 epidemic models.

This post by Mark Draughn at Windypundit was originally published at How to Criticize an Epidemic Model

Dr. Fauci and company told President @realDonaldTrump we were going to lose 200,000 to 2M people as a result of #coronavirus. Today @NIH revised those numbers to about 60,000. 17M people have lost their jobs and our economy has been decimated. Why is #DrFauci still there?

— Bernard B. Kerik (@BernardKerik) April 9, 2020

Dr. Fauci and company told President @realDonaldTrump we were going to lose 200,000 to 2M people as a result of #coronavirus. Today @NIH revised those numbers to about 60,000. 17M people have lost their jobs and our economy has been decimated. Why is #DrFauci still there?
— Bernard B. Kerik, @BernardKerik

First of all, for someone who’s so angry about epidemic models, these people sure are eager to use an epidemic model to make their point. As I write this, about 20,000 Americans are reported to have died from Covid-19 infections, so that figure of 60,000 is just a prediction someone made. Kerik hasn’t cited his figures, but I’m guessing that most people complaining about model estimates near 60,000 are taking that figure from the popular IHME model, which currently has a central prediction of 61,545 deaths (with a 95% confidence interval of 26,487 to 155,315). So these people are getting angry about a model prediction because of another model’s prediction. And even by that prediction, we’re only about 1/3 of the way into the death toll from the first wave of the epidemic.

Nobody says COVID-19 is not real, that it can't tax hospitals or kill people, esp. if they are over 75 or have comorbidities. But right now the best CURRENT projection is for 61,000 US deaths. That was the 2017 flu season. Why have we shut the country?https://t.co/OMStr4jd6i

— Alex Berenson (@AlexBerenson) April 9, 2020

Nobody says COVID-19 is not real, that it can’t tax hospitals or kill people, esp. if they are over 75 or have comorbidities. But right now the best CURRENT projection is for 61,000 US deaths. That was the 2017 flu season. Why have we shut the country? https://cdc.gov/flu/about/burden/2017-2018.htm
— Alex Berenson, @AlexBerenson

As everyone keeps pointing out, shutting things down is the reason the projections are at 61,000. The IHME projections are based on the assumption of shutting down. It literally says “COVID-19 projections assuming full social distancing through May 2020” at the top of every page of the projection visualization.

It’s certainly possible the model overestimates the benefits of the shutdown, but if you object to that assumption, it’s logically incoherent to try to support your argument with numbers produced by a model using the very assumption you’re trying to dispute.

The most overly broad response I’ve seen so far is from Senator John Cornyn:

After #COVIDー19 crisis passes, could we have a good faith discussion about the uses and abuses of "modeling" to predict the future? Everything from public health, to economic to climate predictions. It isn't the scientific method, folks. https://t.co/OYBm3CIUxX

— Senator John Cornyn (@JohnCornyn) April 10, 2020

After #COVIDー19 crisis passes, could we have a good faith discussion about the uses and abuses of “modeling” to predict the future? Everything from public health, to economic to climate predictions. It isn’t the scientific method, folks. https://en.wikipedia.org/wiki/Scientific_method
— Senator John Cornyn, @JohnCornyn

Here’s the problem with what the Senator is saying: Every time you plan for the future — figuring out if you can afford new car payments or deciding when to take your skiing vacation — you are basing your plan on a model. You have some mental idea of your future income and expenses, or of seasonal snowfall at your favorite ski resort. You may not give your model a name or write out equations or implement it in software, but it’s still a model.

And it’s not like there’s an alternative to using models. Economist Paul Krugman wrote a column about “accidental theorists,” people who scoff at academics and others for talking about abstract theories and simplified models. They claim they can understand the world and figure out what we need to do by “looking at the facts” and using “common sense.” But figuring out what to do requires making predictions about the future, and the future hasn’t happened yet, so we don’t have any facts. So by necessity these people are using a theory, but it’s one they have constructed without care, rigor, robustness, or testing…and apparently even without conscious knowledge that they are using a theory.

In the Wikipedia article “Scientific Method” that Cornyn links to, it mentions “formulating hypotheses.” A hypothesis is a type of model, and the formal scientific method is the means by which we test those models against reality. We do that because if we can build a model that describes known reality accurately, we can probably use it to make useful predictions about the as-yet-unknown reality of the future.

(Really bad theories are little more than wild guesses, but even wild guesses can be right some of the time. If you bet a number on a roulette wheel in Las Vegas, you have a 1 in 38 chance of winning, which means you will probably lose. But if enough people play any given spin of the wheel to cover all the numbers, someone will win and get real excited about it. When the Covid-19 epidemic in the US is over and done, and we get a final number on the death toll, some epidemiologist, pundit, or madman out there will turn out to have predicted that number, and they will get really smug about it.)

In her book, Lost in Math, physicist Sabine Hossenfelder explains why physicists use math, and it serves well as an explanation of why all kinds of scientists build models:

In physics, theories are made of math. We don’t use math because we want to scare away those not familiar with differential geometry and graded Lie algebras; we use it because we are fools. Math keeps us honest—it prevents us from lying to ourselves and to each other. You can be wrong with math, but you can’t lie.

[…]

Using mathematics in theory development enforces logical rigor and internal consistency; it ensures that theories are unambiguous and conclusions are reproducible.

[…]

There are other reasons we use math in physics. Besides keeping us honest, math is also the most economical and unambiguous terminology that we know of. Language is malleable; it depends on context and interpretation. But math doesn’t care about culture or history. If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.

When you build a model with math, implement it with algorithms, and publish the data, you’ve built a tool that other people can examine and critique and improve upon. And if it’s a good model, they can use it to make important decisions.

To see what all the fuss is about, let’s take a closer look at the IHME model that everyone’s talking about. It’s based on the general observation that when an epidemic hits a population, the death rate starts with just a few people and then explodes at a furious pace for a while until it peaks, after which it begins to decline until the death rate finally reaches zero and the epidemic is over. If you plot the number of deaths per day, it looks like a bell curve:

The IHME model assumed the Covid-19 death toll would follow a similar curve, but that alone is not enough. To make the model useful, you need to know more about the shape and size of the curve. How high is the peak (the maximum death rate)? How wide is it (how long does the epidemic last)? Are the sides really fast and steep or are they slow and shallow (how quickly does the virus spread)? The model itself is described in an equation (in this paper) and the answers to these questions are parameters to the equation.

To get these answers, you need data about the Covid-19 epidemic. The problem is that this is a brand new outbreak, so we have no historic data on how it behaves. All we have is what’s happening right now. and at the time this model was created, there was only one place in the world which had been far enough through the epidemic for scientists to have data about the shape of the bell curve: Wuhan, China.

In other words, the first version of this model implicitly assumed that the Covid-19 epidemic would follow the same pattern in the United States that it followed in Wuhan. The model does include adjustments for differences in age structures between Wuhan and US locations and differences in some social distancing measures, but it doesn’t account for lots of other differences such as population density, the prevalence of lung disease, or use of public transport.

But just understanding the shape of the Covid-19 model bell curve is not enough. In order to predict when the Covid-19 epidemic will peak in a particular region of the US, you have to gather data on Covid-19 death rates from that region. This data is incredibly messy: Health departments have different standards for what counts as a Covid-19 death, they miss reporting days, or they are late counting reports and some of the day’s deaths get reported the next day. Sometimes they go back and revise old reports. Anybody who has worked with raw data sets knows they always have problems like this.

But from that mess, model makers try to find usable data from which they can construct a local piece of the initial curve of the epidemic in that region. Then they try to match that curve to the shape of the full Covid-19 model bell curve to figure out where that region is on the Covid-19 model curve. Once they know that, they can use the model bell curve to calculate an estimation of when that region’s curve will reach the top and how high it will be, (i.e. how fast people will be dying). They can also estimate the area under the curve, giving them an estimated number of fatalities.

If that doesn’t sound like it will produce a very accurate prediction, you’re right. The IHME model authors are quite clear about this. They discuss problems with the model in their paper and on their website. Moreover, the error ranges in their results are huge. You know how when you see poll numbers, you often see an error range that looks something like “+/-3%”? That means that there’s a 95% chance that the actual number is within plus or minus 3 percent of the poll result. (I’m simplifying a bit.)

Well, the first IHME prediction was for 81,114 deaths, but the error range was from 38,242 to 162,106. (I have no idea which model predicted 250,000 deaths, but it was never this one.) That’s a confidence interval of -53% to +100%. The authors are careful to mention these confidence intervals almost every time they mention any model output, and the visualizations feature the error intervals prominently as shaded regions around the central predictions:

One of the reasons the range of the prediction is so huge is that the early death toll typically follows an exponential curve. It’s like compound interest, except instead of doubling in years, the death toll from Covid-19 has been doubling roughly every 3 to 6 days, depending on the region. That’s incredibly fast, and it makes predictions difficult. If the virus speeds up replication just a little and gets in just one extra doubling before it stops, that’s twice as many deaths.

Since the IHME first published this model, it has been revised several times. By now, 19 locations appear to have reached the top of their bell curves, giving the model a much more accurate and robust picture of the shape, and variations, of the Covid-19 bell curve. (And alleviating concerns about relying on the accuracy of the Wuhan data.) In addition, the model now has two more weeks of data on death rates in the US, which allows for a more careful fit of each region. (They’ve made other refinements as well.)

Finally, note that although the central predictions from this model started at around 80,000 deaths, shot up to over 90,000 deaths, and then came back down to about 60,000 deaths, both the high and low figures are well within the confidence interval of the original model result.

Epidemiologists have been building models of epidemics for over a century, and they’ve gotten pretty good at it. Compared to sophisticated modern modeling techniques (which I can’t claim to understand), the IHME model’s simple curve fit is almost absurdly primitive. But the problem with sophisticated models is that they have a lot more adjustable parameters describing the behavior of the infectious agent and the affected population, which means they require a lot more data to tune the model accurately enough to make it useful.

This epidemic has only been going on for four months, so a lot of the data hasn’t come in yet. With over 1.7 million people confirmed infected and over 100,000 dead, the data is out there, but a lot of it is sitting in hospital files and health department reports from different locations using different reporting protocols. Statisticians will need to spend a lot of time wrangling this data to build a data set that is accurate, consistent, and useful.

I think it will probably take years to get a complete picture of what happened in these first few months of the Covid-19 pandemic, but I hope that well before then we will have enough data to start building more sophisticated models. With the right kind of models, we should be able to estimate the effects of different strategies for monitoring and intervening in the Covid-19 epidemic, which will make the fight a little easier.

This post by Mark Draughn at Windypundit was originally published at A Brief and Unnecessary Defense of Epidemic Models

I enjoy reading your work, really I do. But my enjoyment depends on the assumption of accuracy. When you describe how an anti-ship cruise missile finds and attacks an enemy warship, I expect your description to be accurate, because part of the fun of reading military techno-thrillers is learning real things about the military and the technology. I understand that you’re writing fiction, and that some guesswork may be necessary when the technology is a secret, or when you’re writing about a planned future weapons system that doesn’t exist yet. But I expect that your guesswork will comport with known technology and, more basically, the physical laws of the universe.

Which brings me to something that at least a few of you appear not to grasp: Satellites cannot orbit over the north pole.

It’s true that satellites can pass over the north pole, but contrary to what some of you think, they cannot stay there. I’ve read several books by different authors who clearly believe satellites can somehow stay on station over the poles. The authors obviously wanted to add some cool space stuff to their air and naval battles, so they wrote about a space station “orbiting over the north pole” or satellites “parked over the north pole.” One of those authors also discusses satellite surveillance in a way that makes it clear he believes satellites can hover over a spot on earth for days at a time.

That’s just not how orbits work.

If a satellite is in Earth orbit, that means it’s going around the globe of the Earth in a circle, over and over. That circle might take it around the Earth from west to east, following the equator, or it might be a circle that goes around the Earth at right angles to the equator, passing alternately over the north and south poles, traveling from north to south on one side of the planet, and then returning from south to north on the other. These are called equatorial and polar orbits, respectively. The satellite’s orbit could be also be inclined relative to the globe of the Earth so that it is neither equatorial nor polar, but somewhere in between.

Basically, an orbit can be placed in any way you can imagine a circle going around a globe, as long as the center of the globe is somewhere in the middle of the orbit. But the orbit cannot just hover over the north pole, or orbit in a tight circle around the north pole, or some other random spot on the globe. I.e. This is not possible:

The satellite has to orbit around center of the entire planet. Everything in orbit is always in motion, and moving damned fast. A typical satellite orbiting at maximum speed just above the atmosphere is probably moving about 17,000 miles per hour. Satellites don’t stay anywhere for long. So when writers of military techno-thrillers start talking about satellites “parked over the north pole” — or imply that they are hovering over any location where the action is occurring for more than the few minutes it takes to pass over — it makes me wonder about all the rest of the technology they’re describing. How many other details are they just making up? Are any of those military tactics for real? Does any of this really make sense? That sort of doubt about authenticity takes away a lot of the fun of reading these thrillers.

Technical Addendum: As some of you may be aware, the preceding discussion is greatly simplified. I tried to limit it to just those orbital considerations that would matter in a techno-thriller.

Probably the first thing to note is that the speed at which an object orbits the earth depends on the height of the orbit. Gravity falls off with distance, so it takes less speed to hold an object in orbit at higher altitudes. In addition, the larger the circle of the orbit, the more time it takes for the satellite has to travel around a full orbit. This is especially important when an object is about 22,236 miles above the Earth, because at that height it will orbit the Earth slow enough that it takes a full day to complete an orbit. If this is an equatorial orbit, then the satellite will follow the rotation of the Earth, staying over the same spot on the equator for an entire orbit.

Schematically, It looks a bit like this: [Click the image to animate.]

That’s called a geostationary orbit, and it is the only orbital solution that allows an object to hover over one location on Earth, and only if that point is on the equator. It’s a very useful orbit for many things. Weather imaging satellites will have a consistent view of their portion of the world, making it easy to observe changes over time. And if you have satellite TV, it’s the reason you can use a fixed dish to receive programs, because you’re pointing the dish at a satellite that’s in geostationary orbit over the equator, so it never changes position as seen from a location on the Earth’s surface.

Geostationary orbit isn’t so good for getting involved in combat, however, because the satellite has to be at a height of 22,236 miles (much higher than it appears in the image above, which is not to scale), which keeps it too far from the action in (or near) the atmosphere. Most of the really clear satellite images you’ve seen have been from satellites just a few hundred miles up at most, so geostationary orbit is a lousy location for a spy satellite. That far away, the resolution would be too poor to see much. It’s also much too far away to fire a missile or laser or kinetic weapon at a target inside the Earth’s atmosphere. I think a satellite at that height can probably see something obvious, like a rocket launch, and I believe that the U.S. military uses a few of them to watch for ICBM launches. And of course the satellites are good for communications. (And I think the U.S. military has some satellites up there just to observe other countries’ satellites.) But generally speaking, geostationary orbit is just not a good location for military techno-thriller action.

If a circular orbit at 22,236 miles high isn’t exactly over the equator, it will still rotate with the Earth, in what’s now called a geosynchronous orbit, then the satellite will oscillate back and forth across the equator, spending equal time in each hemisphere, and swinging north and south equal distances. (It will also oscillate east and west as it moves, so it traces out a figure-8 on the surface.)

[Click the image to animate.]

If the orbits are much closer to the surface, then they orbit a lot faster and become useful for spy satellites and other interesting military purposes. And while the orbits follow the same path through space every time around, the Earth still rotates beneath them, so the orbital track on the surface moves westward with every pass, meaning the satellite eventually gets complete coverage of all of the the Earth between its highest latitudes on each side of the equator. In the extreme case, the the orbit is tilted away from the equator at 90-degrees, meaning it will go over both poles on every pass and the Earth’s rotation will allow it to cover the entire planet as it rotates underneath the satellite’s fixed orbit.

While satellites have to orbit the center of the Earth (they stay in a plane that passes through the center) those orbits don’t have to be circular. They can eccentric, which means that the orbit is elongated from a circle into an ellipse, with one end of the ellipse higher than the other. The highest point of the orbit and the lowest point of the orbit will be on opposite sides of the Earth. If eccentricity is zero, the orbit is just a circle, but as eccentricity increases, the more eccentric the orbit is, the greater the difference between the high and low sides,

As satellites fall inward, they accelerate and whip around the Earth at their lowest point, called perigee, at their highest speed, and then slow down again as they rise up out of the gravity well, reaching the top of their orbit, called apogee, at their lowest speed. This gives them a lot of hang-time at their highest altitude, and if they are in a highly-inclined orbit, they will hang out over the high latitudes, which can be useful for surveillance, especially if several satellites are timed so that at least one is always over an area. In this sense, I suppose satellites can — not exactly hover — but at least increase the amount of time they are observing an area, albeit from a high altitude that reduces resolution of things happening on the ground.

(The same principles apply to orbits around the Sun. Halley’s comet, for example, is on a highly eccentric 75-year orbit around the sun, approaching to as close as 55 million miles — which is when it may be visible from Earth — and then receding to a distance of more than 3 billion miles, for an eccentricity of 0.96714. There are a large number of comets in eccentric orbits like this, and they spend much of their time in slow distant arcs far from the sun, some only returning to near the sun over periods of hundreds or thousands of years.)

As mentioned, if the eccentricity of a satellite’s orbit is between 0 and 1, it follows an orbit that is shaped like an ellipse, with the body being orbited located at one of the mathematical focal points of the ellipse. (Technically it is the center of gravity of the two-body system that is located at the focal point. But when one of the bodies is a spy satellite and the other is the entire planet Earth, the difference between the center of the Earth and the center of gravity of the Earth-spy satellite system is negligible.)

When the eccentricity hits 1, things get interesting, because the “high” part of the orbit becomes infinitely high. At an eccentricity of exactly 1, the orbiting body starts from far away and falls toward the Earth, passing it on one side, whipping around through its point of closest approach, and then leaving the way it came, never to return. As the eccentricity grows larger than 1, the arriving and departing paths spread wider apart, so that an object arrives from one direction and departs in another. This is called a hyperbolic orbit.

The hyperbolic orbits we’re most familiar with are those we create ourselves when we launch deep space probes to other planets. These only have the departing portion of the hyperbolic curve, and are commonly called escape orbits since the objects in question never come back. They basically start at the low part of the orbit when we launch them into space at the edge of the Earth’s atmosphere, and then we use booster rockets to accelerate them into hyperbolic orbits so they can leave the Earth and head for distant planets. In a few cases, these objects are following orbits that will leave the solar system entirely, so they are following the departing leg of a hyperbolic orbit around the Sun.

It’s possible to launch a satellite into hyperbolic orbits that leave the Earth on a path that is roughly in line with the Earth’s axis of rotation, so that it departs along a line more-or-less straight up from the North pole. (The conceptually simplest way to do this would be to fire them straight up from a launch pad at the pole, accelerating them until they reach escape velocity.) If the satellites are going fast enough, they will rise higher and higher and never return, all while staying above the north pole. In that sense, an object could be technically “in orbit over the North poll,” but it would be a very weird orbit that quickly puts it thousands and eventually millions of miles above the pole. That’s not the sort of trajectory would be useful for a spy satellite or a weapons platform or anything Earth-related. That’s the beginning of a deep-space flight.

This post by Mark Draughn at Windypundit was originally published at A Brief Note To Military Techo-Thriller Writers

I’ll admit that letting 3000 people die sounds like something Trump would do, but that’s not actually what the study shows. It’s not an evaluation of the relief effort, and it doesn’t attempt to assign blame for any deaths. The study concludes that 3000 people died as a result of the hurricane, but it doesn’t have much to say about the specific causes of their deaths. In fact, the Milken press release announcing the study specifically says:

Additional research must be done to understand how the hurricane was involved in the excess deaths identified in this study. This would involve interviews of family members and others, as well as in-depth statistical analyses, to learn about the circumstances leading up to individual deaths. 

It’s important to realize that this study does not address the effectiveness of the relief effort. This study is about the inclusive death toll from the hurricane. That would include any deaths caused by an inadequate relief effort, but the study does not and cannot separate out those deaths from any others. So while the Trump administration’s relief effort might have contributed to the excess deaths described in this study, the study itself is silent on the matter.

That doesn’t mean Trump supporters are right about the study either. Let’s start with Trump himself:

3000 people did not die in the two hurricanes that hit Puerto Rico. When I left the Island, AFTER the storm had hit, they had anywhere from 6 to 18 deaths. As time went by it did not go up by much. Then, a long time later, they started to report really large numbers, like 3000…

— Donald J. Trump (@realDonaldTrump) September 13, 2018

“3000 people did not die in the two hurricanes that hit Puerto Rico. When I left the Island, AFTER the storm had hit, they had anywhere from 6 to 18 deaths. As time went by it did not go up by much. Then, a long time later, they started to report really large numbers, like 3000…” –@realDonaldTrump

These deaths were not reported immediately because they did not happen immediately. And nobody reported the numbers until a long time later because it took a long time to gather and analyze the data. Public health studies take time.

…..This was done by the Democrats in order to make me look as bad as possible when I was successfully raising Billions of Dollars to help rebuild Puerto Rico. If a person died for any reason, like old age, just add them onto the list. Bad politics. I love Puerto Rico!

— Donald J. Trump (@realDonaldTrump) September 13, 2018

…..This was done by the Democrats in order to make me look as bad as possible when I was successfully raising Billions of Dollars to help rebuild Puerto Rico. If a person died for any reason, like old age, just add them onto the list. Bad politics. I love Puerto Rico! — @realDonaldTrump

The Democrats are certainly trying to make him look bad, but that doesn’t make the study wrong, and the study was not exactly done by the Democrats. It’s not hard to understand why Trump thinks this way, however, when you look at what other people are saying. Here’s Lou Dobbs’s nearly logic-free take:

#FakeNews– The Hurricane Maria death tolls have been inflated & President @realDonaldTrump was right to call out organizations who threw out science and statistics to try to discredit his administration. #MAGA #TrumpTrain #Dobbs pic.twitter.com/xXjF3dfgcH

— Lou Dobbs (@LouDobbs) September 14, 2018

Picking a few choice bits,

The President, by the way, is right. The study the president alluded to is one produced last month by the Milken Institute at George Washington University. Almost a year later, the number went from 65 people killed to 2,975 people, attributed to the storm.

Dobbs is clever with words. Saying “almost a year later, the number went from” implies that there’s some kind of trickery about the delay, rather than the boring truth that it takes time to do public health studies.

The finding wasn’t the result of a death toll count, a body count, nor a study of death certificates, but a public health study that subtracted the number of people who theoretically should have died over the same period from the number of people who were reported dead over that period.

This is why I called Dobbs take almost logic-free. He’s accurately described the study, but then he does nothing with it. He simply pronounces it wrong without ever actually making an argument.

After the report came out on August 28, last month, Puerto Rico’s Democratic governor officially revised the death toll from 65 to the new estimate. And why did he choose to Trust that study? Why not the Harvard study back in June, that found deaths related to the hurricane fell within a, well, a narrow range…are you ready? A narrow range from about 800 to 8000 people. By the way, that’s also an abstract and unconnected-to-any-evidence estimate, that even the liberal Washington Post found ludicrous.

The declaration that these two studies are “unconnected to any evidence” is simply false. The Harvard study was based on a geographically distributed random sampling of over 3000 households which gathered data about 9522 people. Based on the number of deaths found in that sample, they extrapolated to obtain rates for the whole island, and from that estimated excess deaths. This methodology is commonly used to estimate deaths when death records are unavailable, such as poor countries and war zones, and it is understood to give only a very rough answer, thus the extremely wide confidence interval.

The more comprehensive Milken study was based on thousands of official death records from the Puerto Rico Vital Statistics Registry (PRVSR), and its confidence range is a much narrower 2658 to 3290, which is probably one of the reasons the Puerto Rican Government prefers it. It’s just a better study. (Also, the government commissioned it.)

The numbers were inflated, and the President was right to call out the organizations who threw out science, statistics, and evidence to discredit the Trump administration.

Lou Dobbs is an ignorant ass. There’s a lot more legitimate science and statistics in these studies than in anything he said. And as for his assertion that the study is an attempt to discredit the Trump administration, the only actual evidence he offers is the original report of 65 dead immediately after the hurricane. And he gets even that wrong: Until the Milken study was released, the official death toll stood at 64.

John Hinderaker at Powerline has his own take, which is equally silly:

This is what is going on: Some “scientists”–read anti-Trump Democratic Party activists–constructed a theoretical baseline of how many deaths would be expected to occur in Puerto Rico during the months after Hurricane Maria. They then compared this baseline to the actual number of deaths, and voila! The actual number was higher than their hypothetical guess by 3,000.

Hinderaker’s use of scare quotes around “scientists” and his accusations that they are “activists” is complete bullshit that he just made up. There isn’t even any need to attack the study to defend Trump, because the study draws no conclusions regarding the Trump administration or the relief effort.

Hinderaker’s description is, however, a reasonably accurate description of the methodology. The only thing I’d add is that the theoretical baseline is produced by analyzing death rates in Puerto Rico in past years (the Milken study goes back to 2010) to produce a statistical model of deaths, and then using that model to project past trends onto the period of the study to estimate the expected deaths.

So all of those deaths–whether caused by cancer, car accidents, or whatever–are attributed to the hurricane. The study doesn’t even attempt to figure out which 3000 excess deaths are caused by the hurricane. These activists have not made any attempt to count the actual number of hurricane-related deaths.

When discussing “all of those deaths,” it’s important to remember that the death toll of 2,975 is an excess figure. From September 2017 through February 2018 (the period of the study) the PRVSR recorded 16,608 deaths. But the statistical model used in the Milken study estimate the expected number of deaths during that period at 13,633. The difference between the actual and projected death tools is where the figure 2,975 comes from. In other words, according to the study, only about 18% of the deaths during that period were caused by hurricane María. The rest were the result of normal causes, “cancer, car accidents, or whatever,” as Hinderaker says.

But that doesn’t change the fact that there was still a higher than expected number of deaths, which raises the question: If the excess deaths were not caused by the hurricane, if they were due to “cancer, car accidents, or whatever,” then why did those causes of deaths increase? If it wasn’t the hurricane, what was it? Hinderaker offers no alternative.

No one would use such a foolish methodology except for political reasons.

This is actually a standard methodology for estimating deaths in public health science. It’s necessary in situations where it is difficult to identify and observe the causal channels.

Estimating the number of deaths from a disease like Ebola is fairly easy: You find people who tested positive for Ebola and who died from Ebola-like symptoms. Count them, and you’ve got your answer.

Estimating deaths from a disease like HIV is a lot more complicated, because people don’t die from HIV. They die from things like tuberculosis, hepatitis C, Kaposi’s sarcoma, non-Hodgkin’s lymphoma, and a variety of other diseases that kill people whose immune systems have been weakened by HIV. It can be hard to untangle the causes in these cases, and scientists have created the Coding Causes of Death in HIV (CoDe) protocol to help decide, in a consistent way, which deaths to attribute to HIV.

Classifying the causes of death can be complicated. Say a person with HIV is taking drugs which can produce vomiting as a side effect, and one day that person starts vomiting while driving, loses control of their car, and dies in a crash. Does that count as a death from HIV?

I have no idea what CoDe says about that scenario, but in general the answer to questions like that depend on why you want to know. If you are an actuary for an insurance company providing group life insurance to a company that employs people with HIV, it certainly counts, since you will have to pay that claim. And if you’re an economist studying the cost of HIV to society, not only would you count that death, but you would also count the collateral deaths of any passengers or pedestrians killed in the crash as well.

With a hurricane, the causal channels are even harder to analyze. The immediate deaths from storm surge, windblown debris, and collapsed structures are relatively easy to identify, but the hurricane also disrupts the infrastructure of civilization, and that can lead to more deaths. People with diabetes could face hazardous disruptions to their food, their insulin supply, and their healthcare. People on supplemental oxygen could lose power for the oxygen concentrators, and delivery of tanked oxygen could be disrupted. Patients on blood thinners could miss blood tests and fail to adjust their dosage correctly. Kidney dialysis centers could be out of power or supplies, forcing patients to travel further for care.

In fact, with random destruction taking out buildings, people will likely have to travel further for everything, and the extra driving alone will kill some people, even before the added risks from driving on debris-strewn roads with no traffic signals or street lights. People will die because they can’t call an ambulance with the phones down, or because the ambulances are all busy, or because the ambulances have to take longer routes to hospitals, or because hospitals are unable to operate at full capacity, or because hospitals can’t get supplies of needed drugs. People will kill themselves trying to salvage property from collapsed houses. People will fall off their roofs while repairing storm damage.

Hurricanes are a mess of causes that are difficult to sort out, which is why this study used a method that doesn’t depend on knowing the cause of every single death. A conceptually similar methodology was used to establish that cigarettes caused lung cancer. When the global lung cancer epidemic hit humanity at the end of the 19th century, nobody knew the cause. The cellular mechanisms of cancer would not be understood for many decades (and are still the subject of research today), so scientists had no way to determine the causal chain that led to lung cancer in specific patients. Nevertheless, by the 1930s scientists had gathered statistical evidence showing that the lung cancer rate was far higher in people who smoked cigarettes than in people who didn’t smoke. By the 1960s, the link was established well enough (even over the obstructive efforts of tobacco companies) to discourage people from smoking and to affect public policy.

The Milken study is similar in concept, except for the choice of control population. Cigarette studies used non-smokers as controls, because they could be drawn from otherwise similar populations. There’s no similar control population for Puerto Rico — no otherwise identical island population that wasn’t hit by a hurricane — so as a control the researchers used the same population that was hit by the hurricane, but from the years immediately before the hurricane.

By this point, someone will be screaming that “correlation does not prove causation!” That’s true, but it can certainly imply causation in a properly done study, especially when accompanied by a good explanatory theory. In this case, the theory is that hurricanes destroy infrastructure, thus increasing the danger to human life. That’s not a particularly controversial theory, and when you observe a hurricane followed by an increase in deaths, that tends to confirm the theory. Critics are welcome to offer better theories to explain the data.

(I should mention that the Powerline post also argues that Puerto Rico’s death rate declined in 2017. I’m not sure where those figures come from, but the IndexMundi source they site appears to get its data from the CIA World Fact Book, which describes the Puerto Rico Death Rate entry as a “2017 estimate.” Furthermore, since the death rate is calculated as the number of deaths divided by the number of people, it is sensitive to changes in the population size, and I suspect this estimate is based on U.S. census estimates of the Puerto Rican population. However, after María struck, about 8% of the Puerto Rican population, 300,000 people, decided to leave the island. That mass emigration did not make it into census estimates, but the Milken study used travel records to adjust its figures to account for the decline in population.)

My regular nemesis, Jack Marshall, also attacks the study:

I’ve covered the revised hurricane death tolls before. Nobody knows what the real figure is, and it is fair to question the newer estimates, which were produced by public health experts at George Washington University in Washington. Their report was commissioned by the U.S. territory’s governor, Ricardo Rossello, and he was looking for big numbers: the more deaths, the more U.S. aid.

That’s no reason to smear the scientists with accusations of falsifying data.

The news media misrepresented the study as well. Here’s Reuters:

[..] The study found that those deaths could be attributed directly or indirectly to Maria from the time it struck in September 2017 to mid-February of this year.

False! the study didn’t “find” that at all. It assumed it; it theorized it; it argued it. There is a material difference between finding something and assuming it’s there.

The results of a study are commonly referred to as its “findings.” Jack is either (1) an ass for pretending he doesn’t know that or (2) an idiot for not knowing that.

Jack also references a blog post by Peter Grant at Bayou Renaissance Man:

I find this study highly suspect. One can find similar increased death tolls in other areas, but with autopsies, witness statements, etc. that make it possible to analyze them properly. Example: the opioid epidemic that’s ravaging several US states at present. Death rates due to the misuse of opioids are climbing dramatically, but in every case, the cause of death can be measured, medically confirmed, and verified. How do we know that opioids weren’t responsible for at least some of the “excess” deaths in Puerto Rico?

I’m sure opioids were the cause of some of the 16,608 deaths in Puerto Rico in the five months after the hurricane, and it’s possible there was even an increase in opioid-related deaths after the hurricane, and if someone can dig up those figures, the Milken institute should probably revise its data (assuming that the increase in opioid-related deaths is not itself due to the hurricane).

What about deaths caused by vehicles? How do you know whether an accident was due to increased traffic, caused by aid distribution after the storm, or a drunk driver? The first might be blamed on the hurricane; the second, certainly not.

Again, the 2,975 deaths are an excess figure, so offering alternative causes of death is insufficient. Any alternative theory for the deaths needs to explain why the death rate for that cause increased when it did. If some of the excess deaths are due to drunk driving (or opioids for that matter), what happened to make the drunk driving rate increase in the months after the hurricane?

Without medical and other evidence, one can’t assign a definitive cause to each casualty; but the study conducted there did not examine such evidence. It only looked at numbers, and made assumptions.

Obviously, the Milken study is not definitive. We could get a much better idea of the death toll from hurricane María if someone did a careful study of each of the 16,608 deaths during this period to determine the cause. Unfortunately, the data just isn’t available. The CDC has guidelines for a special death certification process to be used after a natural disaster which would have gathered some of the needed data, however the Milken study reports that those guidelines weren’t followed in Puerto Rico, largely due to lack of training of medical personnel and poor communication by authorities. In addition, the PRVSR offices were damaged by the hurricane, and death certificate filings were substantially disrupted.

To gather the necessary data now would require defining a protocol and training a team to review medical records and interview friends and family members of the deceased to determine the complete causal chain leading to their death. That’s the (very expensive) study you’d need to do to lay this question to rest.

But no one has done that study, or any study better than this one. So until someone does, the Milken study remains the best and most accurate attempt ever made to estimate the death toll from hurricane María.

This post by Mark Draughn at Windypundit was originally published at On the Puerto Rico Hurricane Study