the "herd immunity" threshold for COVID-19 is probably around 60% of the population. no country is anywhere near this.

"herd immunity" is not a magical concept. let's talk about what it means. 1/n https://twitter.com/koaleszenz/status/1291092182246588416

there are a few folk versions of "herd immunity" going around. it is difficult to disentangle them. some people seem to think groups of hosts simply become resistant (lower death rate) over time: others think unexposed members of the population mysteriously become immune. 2/n

"herd immunity" is, broadly speaking, a state where a large enough number of potential hosts, either due to vaccination or past exposure, are no longer able to contract an infection, such that the infection is no longer viable and cannot spread further in the population. 3/n

a simple model: suppose an infected individual goes on to pass their infection to r susceptible members of the population, on average. if r is less than 1, then on average, the total number of infected individuals will decrease. if it's greater than 1, it will increase. 4/n

it is easy to see that r will, technically, decrease over time as hosts recover and become immune, so epidemiologists often refer to r_0, which is the value of r in a population consisting entirely of susceptible individuals. i'm just going to call it r for brevity. 5/n

suppose that r' is the effective value of r in a population where a fraction p of individuals has been infected. then:

r' = r(1-p)

6/n

we need r' to be less than 1 for the virus no longer to be able to effectively spread. thus:
r' < 1
r(1-p) < 1
1-p < 1/r
-p < 1/r - 1
p > 1 - 1/r

that is, if a fraction p = 1 - 1/r of individuals are immune, the virus (in theory) cannot spread. 7/n

for COVID-19, r is somewhere between 2 and 2.5. thus, p is somewhere between 0.5 and 0.6, meaning 50-60% of the population needs to be infected to achieve herd immunity.

no country on earth is anywhere close to this. 8/n

by the way, compare this to a virus like measles, for which r is closer to 18 and hence p is about 0.94. now you understand why small clusters of anti-vaxxers can lead to localized measles outbreaks. vaccinate your kids. 9/n

anyway, a common feature in epidemiological models is "overshoot". when a pathogen is spreading in a population, it is likely to ultimately infect more hosts than are strictly speaking for herd immunity. 10/n

ongoing epidemics do not magically stop when the threshold has been reached. i was going to include a detailed explanation of "overshoot" here, but i wouldn't explain it as well as carl bergstrom does in this thread, plus i'm lazy, so just go read it: https://twitter.com/CT_Bergstrom/status/1252000688239816704 11/n

it is theoretically possible to achieve herd immunity with a smaller fraction of individuals: for example, on a network, individuals with a high number of connections may be infected earlier, rendering them immune and hence unable to transmit later. 12/n

however, it is probably better to think of the baby math herd immunity threshold we just calculated as a best case scenario. the final number of infected individuals is not p = 1 - 1/r but rather more like the solution to p = 1 - e^(-r*p), which is much higher. 13/n

source for that equation: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3506030/ 14/n

"overshoot" is a very real phenomenon: if any government (say ours) were stupid enough to adopt an unmitigated herd immunity strategy, as many as 30% of the deaths could be plausibly due to overshoot. that could be millions of people. 15/n

tl;dr: wear masks, be a responsible citizen, and don't spread stupid bullshit about sweden having achieved herd immunity. you are wrong and you are possibly going to get people killed.

n/n