04 April 2021

Rₜ, R₀, and vaccination

There's a "nothing in real life is ever this simple" formula about what fraction of the population needs to be immune ("have a robust immune response"), before you can stop worrying about the spread of a disease:

If R₀ (or Rₜ) is 5 (in the vicinity for wild-type COVID-19), you need 80% of the population to have a robust immune response to keep the disease from spreading using herd immunity alone.

If R₀ is 10, which is not implausible for some of the observed COVID-19 variants, you need 90% of the population to have a robust immune response to keep the disease from spreading using herd immunity alone.

Knowledgeable people who are not doing the "nothing is ever this simple" version are saying things like "at least 85%" about the necessary vaccination level for herd immunity; the current vaccination rates, even in the US, aren't anywhere close to enough to keep the disease from spreading.

If 85% vaccination is required to get to herd immunity, we can't get there this year; at least twenty percent of the population is too young to be given any current COVID vaccine, even if absolutely every adult gets vaccinated with an mRNA vaccine.  Approvals for use as paediatric vaccines are being sought for all the COVID vaccines, but right now the age cutoff is 18.  Several of the vaccines can't get to 85% effectiveness, either; so far only the mRNA vaccines have effectiveness levels high enough that, in principle, vaccinating absolutely everybody would be sufficient to extirpate the disease.

We know, from several national examples of effective public health, that you don't need a vaccine to extirpate the disease; you can institute movement controls, food delivery, necessary "hold in place" payments so people can not work and not starve, enforced quarantines, and a robust track-and-trace system, and extirpate the disease that way.  It'd be really expensive to do that now, rather than in the beginning, but it could be done.  Effective public health measures are not being done as a matter of deliberate and conscious profits-before-people policy, targeting reopening rather than extirpating the disease.

The variants now spreading affect children and young people more seriously than the wild type.

We can expect, if we treat some level of vaccination -- any level of vaccination we can achieve this year -- as grounds to generally drop COVID restrictions,  that we will see the continued spread of the disease.  It will produce many more dead children compared to the wild type, and it will (given the Brazilian example) put vaccinated people into hospital, possibly in large enough numbers to overload the system.  (The system overload threshold is decreasing over time, as health care personnel are being expended by the strain.)

What the vaccines accomplish, even the "this won't stop spread" vaccines, is to greatly reduce your odds of harm if you should contract the disease.  You are much, much less likely to die or to require hospitalization.  This is useful and worthwhile; by all means get vaccinated.  Just remember that this is a personal-scale benefit, not a systemic solution.

The other thing the vaccines do, because they are not sterilizing vaccines, is increase the odds of worse variants developing in a given individual; more infectious variants arise when the virus spends a long time reproducing inside one host.  That is, the virus and the host's immune system stalemate, and the virus reproduces many more times than usual, increasing the odds of a mutation that increases virulence happening.  This is a big part of why you don't want people catching the disease in the first place and why the "just let it burn through the population and it's over" take is extremely dangerous.  The sixty percent vaccination rate that's guessed as the eventual full voluntary uptake is, as the sole public health measure, a recipe for worse COVID.

The policy that comes out of this ought to be:

  1. vaccinate everybody as soon as possible, starting with the people in the groups most likely to catch the disease
  2. adopt the full public health measures, including movement controls, enforced quarantine, and a required complete economic shutdown so people can stay home
  3. an explicit requirement that reopening happens if and only if the disease is extirpated; no level is acceptable
because otherwise we're just going to keep going round and round in this merry dance.

(There's a political truism that things mostly go away on their own, if you just wait a bit.  That's not true of diseases, and it seems rather difficult for a lot of politicians to absorb that it's not true of diseases.)


D. C. said...

Yes, politicians expect most things to go away of themselves. Humans are very good at adapting to an amazing range of utterly horrible conditions.

Politicians (and that includes lawyers) on the other hand, are accustomed to creating the realities that we live in. Don't like a law? Change it. Or get a court to overturn it. Or maybe you solve a pandemic by lying about it and telling people that it's a hoax, no worse than seasonal flu, etc. They think nothing of setting the age of the Earth at 6000 years, dinosaurs as contemporary with humans, petroleum as being continuously created, mammalian species as absolutely binary gender, etc. ad nausea.

So it's hardly surprising that they should end the pandemic by fiat. We will undoubtedly adapt.

Graydon said...


Well, on the assumption that various COVID variants become endemic, you get it every couple-three years, and it retains the overall 1% chance of killing you per infection, that gives about 9% of the population dead in one generation, 25 years. (0.99^9)

If it's 2% chance of killing you (which various variants already exceed), that's be 16% of the population in that same generation. (5% is 37% in 9 illness; 10%, the lethality of SARS, kills more than 60% of the population in that time frame, but surely even mammonite politicians would consider the utility of public health measures in such circumstances.)

Even the 1% version is not an outcome conducive to the maintenance of social order, especially while the collapse of agriculture is accelerating and these other societies over there have extirpated the disease.

D. C. said...

Meanwhile we ignore Long Covid disability (too little data is no excuse), which over time both increases net mortality and economic losses.

Of course mammonite rulers would consider mortality generally acceptable, along with other forms of turnover. Long Covid would probably inspire culling in one way or another.

As we've seen with the response to warming, "It's too late to prevent and/or too expensive to do anything now" is another way of "solving" a problem by fiat.

JReynolds said...

Cory Doctorow commented yesterday (tongue in cheek) that it's strange how Doug Ford, who has actual experience dealing drugs (hash, in DoFo's case), is doing such a poor job of getting drugs to people.

I'm looking forward to eventually getting my shot. No idea when this will be for the 50-54 year age group.

Graydon said...


It'd be more accurate to note that Dougie has a lot of experience taking a cut of the cashflow from selling drugs, rather than ever actually selling them himself.

(Which I think is relevant; it's visibly causing him pain he can't charge people for COVID vaccination.)

For planning purposes, I kinda doubt we are going to get vaccinated or that Phase 3 as such will happen. It's going to take real spend to make even Phase 2 happen, and it's clear the money is not forthcoming.

Graydon said...


Economic losses are fine, too, as long as the particular mammonite experiences no relative loss. "But of course they want a large economy, they want to be rich!" does not actually follow; they don't want to be rich, they want to be richer than you, which proves God loves them more.

The rest, yeah, I think you're correct about all of that. Going to be a job of work.

heron61 said...

The data for the mRNA vaccines protecting 12-17 year olds looks (from what I've read recently) sufficiently good, that they could easily end up being vaccinated within the next 3-6 months, which isn't the same as everyone, but (at least in the US) 11 and under kids are around 15% of the population, so we could get close.

Seruko said...

I'm not sure about the science, but I do know the defacto truth on the ground . States are vaccinatING 16 and up FWIW. Also any hope for a new novel 2021? I could use some utopian magic competency fic, just to get me through the dark time you know? Maybe a short story or a novella? I'm hard upan, I'm in real pain here.

Graydon said...

+heron61 Close if and only if you manage to convince white evangelicals to get vaccinated. If not, it's going to be taken as proof vaccination isn't real because the disease will still be circulating.

Graydon said...


That's likely the correct decision under the circumstances. It's not enough to make a difference in terms of actually extirpating the disease, though, even without considering that many adults won't voluntarily vaccinate.

These are absolutely amazing vaccines; they're still not sufficient, in terms of induced immune response, nor (likely) in length of protective effect, to extirpate the disease on their own.

Graydon said...


Nothing, book wise, is expected this year. (Day job is very busy, which is useful for avoiding dying in a ditch and much less useful in time-to-write respects.) Progress is continuing, though, so sometime.