Sunday, September 26, 2021

By the Numbers

I have seen the argument advanced in a few places that getting lots of people vaccinated is actually more dangerous, because it creates a more likely opportunity for a super-variant of Covid to arise, one that overwhelms even vaccinated immune systems. While this is not so, it does have an element of truth in it that deserves refutation rather than mere dismissal.

Let us look for a moment at winning a lottery.  A person who has bought a million tickets has a much better chance of winning than a person who bought only one, so his average expected winnings is a million times higher.  But there aren't really "average" winnings in a lottery (a pure lottery.  I am excluding the actual money-raising games that give lesser prizes for getting some of the numbers right). If you win the 10 million dollars, you win it, and if you don't you get nothing.  The idea of average winnings is something of a statistical trick.

The rise of a supervariant is like a lottery in reverse, an enormous single bad-luck outcome. If everyone but one person were vaccinated, there would still be a chance, however minuscule, that the last person who contracted the disease carried a mutation that turned out to be the supervariant that overwhelmed everyone else. You can see how that might happen in theory, but no one is losing sleep over that possibility.  Much more worrisome is the situation where there are many, many people carrying the virus.  It's like millions of lottery tickets for that ugly reverse lottery. Even though the chance of a supervariant mutation is extremely low for each of those "tickets," in aggregate the odds are much greater.  It is still small.  There have been millions and millions with the virus, and only a couple of variants that have been problems.  It may be that only the Delta is a big deal.There are likely many mutations out there already, but as well all know, most mutations make things work worse, not better.  The many mutations simply sink beneath the waves.

But if there are a bunch of these mutations around, they have an enormous number of vaccinated targets.  I am going to describe the situation as if the virus is "trying" to outwit the potential hosts, even though it is not sentient and trying to do anything.  It's just with such enormous numbers it has that appearance, of an organism trying to get through defenses, like a hundred million squirrels trying to get through to the bird feeder by indefatigable persistence. When there are only a small number of variants, it's like there are fewer squirrels trying their hand at the obstacles.  The odds of the squirrels in general succeeding and coming up with a strategy is low.  But when there's lots of squirrels, the possibility that one might hit upon the one brilliant strategy is increased.

I don't know what the worst ratio is for that possible development of a supervariant is, but I have to think 50% vaccination - right about where we are now - might be close.  With 95% vaccination, there just wouldn't be enough squirrels working at the feeder puzzle.  But with 50%, there are a huge number of people carrying the virus, and they have a huge number of targets - both the easier targets of the unvaccinated and the hardened targets of the vaccinated. Or if you prefer, while one of the few unvaccinated in the 95% scenario might develop the winning ticket variant that is actually the losing ticket variant for us all, such a variant is more likely to arise in the scenario of only 50% vaccinated, because that would be like buying ten times more tickets for that lottery.

Even with all the unvaccinated counted together a supervariant might not arise. Even though it's ten times worse than the 95% vaccinated scenario it's still low.  But remember, the original predictions months ago were that more powerful variants were unlikely - and we've already had one.  Worse, the one we've got is still spreading, so a variant of that would only have to be a little worse to be a heightened risk. We don't actually know the likelihood.  No one does. It may be unfortunate bad luck that we got even one Delta variant.  Or we may have gotten lucky with ten almosts that just missed, with no reason to expect such good luck in the future.

It has some importance because of the insistence of the unvaccinated that they represent no danger to the vaccinated, and so should be left alone by all the busybodies. It is true in the limited sense that the potential danger of each unvaccinated person is low. Like lottery ticket low. Though someone does eventually win lotteries, and if you buy millions of tickets the aggregate danger is higher. At minimum, they increase the risk of danger for us all.

If someone has better math on this, let me know.


Fo4Ho1 said...

My math is I have two choices.

Christopher B said...

The best environment for a virus is as a symbiotic parasite that doesn't kill its host. From all evidence available, vaccinated people are as likely to be hosting SARS2 as non-vaccinated. It doesn't make them sick, and their bodies may clear the virus but 'breakthrough' infections indicate that doesn't necessarily happen before they spread it. Mutations are going to happen, just like the 1918 influenza developed even though we have a similar level of natural immunity to influenzas in general.

The best argument for vaccination remains personal protection from severe disease and hospitalization.

Assistant Village Idiot said...

My understanding is that one is far less contagious when vaccinated. I will recheck, but feel pretty confident of that.

Assistant Village Idiot said...

As for the first comment, I have a guess what it means but am not sure. Fo4Ho1, are you saying that because you legally have two choices, one is as good as the other regardless of the evidence and no one should contradict you?

David Foster said...

Not obvious why a 50-50 mix of vaccinated and unvaccinated would be any different, in terms of variant evolution, from a 50-50 mix of those with natural (acquired) immunity and those without such immunity.

Assistant Village Idiot said...

Yes, any 50-50 would do. They are likely equivalent immunities, though differences may emerg. The number of Americans who have had the disease is about 40 million, which is a large number. The number of vaccinated is I think about four times that, which causes me to all-too-frequently neglect the other. Good correction. And the number who have had the disease may turn out to be higher, even much higher.

Cranberry said...

Harvard has just moved its 1st year MBA students online, due to a Covid cluster among graduate students at the Business School. 95% of students are vaccinated.

Cranberry said...

Breakthrough cases in the vaccinated are a thing. One of our children just had a breakthrough case at college, verified by a test. He had a mild, cold-like illness with a fever.

Harvard is testing frequently, so it's catching cases among people who don't think they have Covid.

I think some of your assumptions may not be true in practice. I assume a certain number of people who get breakthrough cases are either asymptomatic, or think that it can't be Covid, because they're vaccinated, or the symptoms are so mild they think it isn't Covid.

In the US, something like 55% of the eligible population is fully vaccinated. The CDC estimates there have been ~42 million Covid cases in the US. I've seen estimates, based on various studies, of about 3 to 4 times as many cases, because many people with mild cases don't bother with a Covid test, especially in the early days when you needed a doctor's orders to be allowed to get a test. Studies that looked at antibody levels in the population at large have found that more people have had Covid than have been diagnosed with Covid. Of course, the vaccinated and the naturally exposed sets overlap.

Nevertheless, I'm not as worried about new variants arising in the developed world, where people can be tested and isolated, even if they are not vaccinated. I'm much more worried about the low-income countries with less than 10% of their population vaccinated, no effective medical system, and crowded living conditions.

A look at the list of variants of concern shows they have so far first been noticed in countries more likely to have such conditions: India, Peru, Brazil, South Africa

However, as vaccination does not stop infection, even if the entire US were to reach Harvard's level of vaccination, the pandemic will continue. Variants that are more infectious to vaccinated people will be selected by evolution, because variants that infect vaccinated people will be more likely to spread.

David Foster said...

Somebody, I think it was at Grim's Hall, observed that if you want to find enemy submarines, you don''t depth-charge the entire ocean. You use sonar, radar, and communications intercepts to find out where the target submarines actually *are*, or at least where they might be.

The Covid analogy is to testing. It is somewhat strange that the US hasn't put more emphasis on developing/distributing tests that can be used at home and provide immediate results. The impact on Covid spread would surely be considerable.

Grim said...

That was Tex, although I think she was responding to an analogy by Richard Fernandez.

Assistant Village Idiot said...

Craig Spencer wrote similar articles for The Atlantic and for Hot Air about the vaccinated spreading covid

I can't touch his credentials and could only argue against him if I was detecting places where he was leaving stuff out or arguing from motive (which I am good at), but this looks solid to me. I have found the people who corrected me here to be quite reliable in the past and hesitate to go against them, but I now feel confident of my original assertion. Vaccination also affects spread, and thus has to affect carrying the virus at some level. A fairly high level, actually.

That many more people might have been exposed I have already granted, and the number might be quite large. However, identifying mechanisms by which this might be possible, that a third of the population might have gotten it and not known it or gotten tested, is not the same as evidence that this actually happened. I also readily believe that breakthrough infection is a thing and have never said otherwise. A lot of what is spreading now is Delta variant, which vaccinations are less effective at preventing, though the number is still quite high, just for openers.

Zachriel said...

Infection among unvaccinated persons were 4.9 those in vaccinated persons.

Zachriel said...

There's also a partisan aspect to COVID. Red states have lower vaccination rates and higher current death rates. This aspect is even more pronounced when seen at the county level.

Vaccination rates and 2020 U.S. election vote shares

Covid deaths and 2020 U.S. election vote shares

David Foster said...

Zach....if you look at state vaccination rates and death rates while holding a couple of other variables constant, you might get some interesting results. It's well-known that black people are less-inclined to get vaccinated than are white people...higher black % in the population might explain much of the lower vax rates for red states. On the other hand, older people are more likely to get vaxed, and some states have much higher % of same.

Simple exercise in regression analysis, or you could even do it with basic crosstabs.

Zachriel said...

David Foster: It's well-known that black people are less-inclined to get vaccinated than are white people

The racial gap has narrowed.

Nor would that explain why the correlation applies at the county level.

Here's a map of median age by state.

Red state Mississippi has a younger, diverse population and red state West Virginia has an older, largely white population, but they both have lower vaccination rates. Meanwhile, blue state California has a younger, diverse population and blue state Vermont has an older, largely white population, but they both have higher vaccination rates. There may be a correlation, but it's not so obvious.

Zachriel said...


U.S. Adults Vaccination Rates by Political Affiliation

Zachriel said...

Here's the county breakdown in California:

Texan99 said...

My county surprised me by having a much higher vaccination rate than the rest of the state of Texas, not only among our substantial elderly population but even among the entire population over the age of 12: both around 70%, per the state's reports. We continue to get a trickle of deaths. I can't find out for sure whether any of the deaths are vaccination break-throughs, but none at least have been definitely identified as vaccinated patients, and all the ones I've been able to ask about specifically were unvaccinated. All so far have also been either elderly, obese, both.

Nor have I heard of any cases who got the monoclonal antibody treatment and still died. The feds clamped down on the supply of this treatment in recent weeks, but Gov. Abbott followed Gov. De Santis's example, thank goodness, and found an independent source. Regeneron reports that only 30% of eligible patients are receiving its treatment, but at least that's an increase from 5% in July. I will never understand why it seems to be so impossible to get word of this treatment out to the general public, or even their doctors. Is it really just that everyone is terrified that mere knowledge of the treatment will discourage vaccine skeptics from coming around? That seems to be the White House's take.

David Foster said...

Zachriel...interesting data, thanks. Do you know if the "vaccination rates by political affiliation" included a reasonable sample of *all* adults?...the rate for Dems seems awfully high at 92%, and I've previously seen data suggesting that "independents" tended to be more anti-vax in general than are either Reps or Dems.

It is somewhat bizarre that there are as many Republicans suspicious of the vaccines as there are, given that we have these vaccines at this point in time largely due to the impetus provided by the Trump Administration. Leaving things to their normal pace, we would have been waiting a loooong time.

I believe that the hectoring/scolding/threatening approach taken by the Biden administration has led to a lot of pushback, and that an approach which was more educational and marketing in nature, and less 'respekt-mah-authoriteh' would have yielded better results.

Thomas Doubting said...

AVI, thanks for explaining this. I really didn't understand it until now.

Zachriel said...

David Foster: Do you know if the "vaccination rates by political affiliation" included a reasonable sample of *all* adults?...

The polling is only a sample, but is supported by the state and county disparties as shown.

David Foster: It is somewhat bizarre that there are as many Republicans suspicious of the vaccines as there are, ...

Trump frequently undercut the messaging on public social policy, often in bizarre fashion.

David Foster: given that we have these vaccines at this point in time largely due to the impetus provided by the Trump Administration. Leaving things to their normal pace, we would have been waiting a loooong time.

The primary work on the vaccines had already been completed, and scientists were ready with the solution. The sequence for SARS-CoV-2 was published in January 2020. The mRNA vaccine only took weeks to create, and initial trials started in April 2020. Scientists thought that the vaccine could be ready for the public by the 1st quarter of 2021.