A while back, when it seemed like a lot of people were becoming ill with covid, I wondered how long it would take to get to herd immunity the hard way. It turned out that, although it seems like horrendous numbers are becoming ill, the percentages of the population were much smaller than I had intuited.

It’s time to do another calculation. IIRC, we didn’t have vaccines when I last did that calculation, and it was before Delta made its appearance. There’s not much talk about herd immunity these days because of Delta’s much higher transmissibility and maybe because it’s gotten mixed up in the “let it rip” crowd. I hope to write a post on R and those calculations one of these days.

I built a VERY simple Excel model. The point is to get a handle on the numbers, and two significant figures are good enough for that. If anything, it may overpredict deaths, which would be a change from our expectations of the last almost two years.

The state population numbers are from the World Population Review. The covid numbers are from last night’s New York Times tracking.

I converted the cases and deaths per 100,000 to percentages. I assumed that 10% of those vaccinated had been infected and removed that overlap. I also assumed that 10% of those vaccinated were still susceptible to serious cases of covid. I added the percent of cases to the adjusted 0.8 of vaccinated to get the immune %. The susceptible are thus everyone else. I multiplied the death percentage times the susceptible (this is probably the largest source of pessimism) to get the expected deaths.

The bottom line, expected deaths for the US, is close to 300,000, which will give a total close to a million dead from covid. That doesn’t count excess deaths from the overloading of the medical system. Combined immunities from illness and vaccination are not too different from the percent of vaccinations. The pandemic is far from over.

Photo: The Guardian

Cross-posted to Lawyers, Guns & Money

This may be simple and obvious, but it’s worth saying.

The more virus there is around, the more danger to all of us, including the vaqccinated. That’s why nonpharmaceutical interventions (NPIs) like masks and distancing are important.

The more virus you encounter, the more likely it is that one of those encounters will go well for the virus and badly for you. So when case numbers go up, it makes sense to take more precautions.

The reason that anti-vaxxers are often able to avoid having their children infected with measles is that there is usually no measles virus circulating. An immune system that can’t handle the virus is safe as long as it doesn’t confront the virus.

This ties into speculation on the endemic endgame for SARS-CoV-2, although I haven’t seen anyone consider it explicitly. We can, through a combination of vaccines, natural immunity, and NPIs, get the virus down to the levels we’re accustomed to with measles. At current rates, however, that will take years. It might be instructive to look at how measles cases declined after vaccination became available.

Cross-posted to Lawyers, Guns & Money

I’ve had a vision of writing a magisterial series to clarify everything about the mathematics of the pandemic, but it looks more like I will, hit-or-miss, do one issue at a time.

I’ve worked with mathematical models for chemical reactions. The math is identical to that of a pandemic – coupled differential equations describing the transformation of one set of things into other things. In the case of the pandemic that transformation is

susceptible people -> infected people -> immune or dead people

Sets of coupled differential equations have become popular for such things since we have gotten enormous computing power. Solving them isn’t easy to do by hand. Epidemiology (and chemical kinetics) grew up with simpler equations to model their processes. And those simpler equations can be good for some things!

I’ve wanted to understand the breakdown of the unvaccinated. How many are hard-core antivax and how many just haven’t gotten around to it for some reason? And who is in each category?

Here’s a source whose data I trust, but they’ve arranged the data in a particularly unhelpful way for my question.

They define a wait and see group, who want to “wait until it has been available for a while to see how it is working for other people” before getting vaccinated and a definitely not group. The wait-and-sees are 12% of American adults, and the definitely-not 13%. The wait-and-sees have been decreasing, but the definitely-not have stayed at 13%.