Thread by @gro_tsen

As I've pointed out a number of times, there is a terribly confusing ambiguity as to what the phrase “herd immunity” (or its synonyms, e.g., “collective immunity”) means. In the SIR model it's the point where R becomes ≤1. But in real life? 🧵⤵️ •1/14

If we use the same definition (R≤1), then herd immunity is pretty much unavoidable. Barring unrealistic mathematical counterexamples, the only alternative is to have exponential growth forever, which, of course, simply cannot happen. •2/14

(“Unrealistic mathematical counterexamples” here acknowledges the fact that you can have R>1 forever but tending toward 1 so the number of infected remains bounded. Even then, you're still tending toward herd immunity.) •3/14

Indeed, with this definition, there are many places on Earth which currently have herd immunity against covid, meaning simply that the number of cases is not rising. Even when it is rising exponentially, everyone realizes that this will stop eventually — somehow. •4/14

Now maybe you want to add the qualifier that all restrictions are lifted to really call it “herd immunity” as opposed to “conditional herd immunity” (explained in the thread below). Even that is unavoidable if, indeed, restrictions are lifted. •5/14

https://twitter.com/gro_tsen/status/1324405641268645888

So if herd immunity is essentially impossible NOT to achieve, why is it that we so often see the claim that “with the δ variant, we can't reach herd immunity”? Well, there are a number of issues which make the term unhelpfully confusing. •6/14

One is that, obviously, we want the “immunity” in “herd immunity” to come as much as possible from vaccination. Now if the vaccine is only so-or-so effective, even vaccinating 100% of the population might not be enough to reach herd immunity. •7/14

(As a side note, the value 1 − 1/R₀ is often given as the fraction that must be made immune to achieve h.i.; so it would be the least efficacy of a vaccine that can achieve it alone. I've criticized this formula, but for vaccination it's sensible. •8/14

https://twitter.com/gro_tsen/status/1373723340226052098

However, we must still remember that R₀ is, itself, a number that should be taken with caution in general, and the values of ~8 given for covid variants are absolutely meaningless junk as I explain in the thread below and those it quotes. •9/14)

https://twitter.com/gro_tsen/status/1405072146636869636

Another issue is that herd immunity, once attained, might fail to be durable. We may fluctuate in and out of it for a number of reasons, e.g., waning immunity, as the thread below explains. •10/14

https://twitter.com/AdamJKucharski/status/1316283049445855232

The limit of this situation is when we have a steady state where, say, the number of people newly infected per unit time equals the number who lose immunity per waning. This is called an “endemic” state. But I emphasize that it is still a facet of herd immunity. •11/14

Indeed, in a simplistic homogeneous SIR-like model (but with waning immunity, or population replacement), the proportion who are immune in such a steady endemic state is given by 1 − 1/R₀ at any given time: immunity is keeping exponential growth in check. •12/14

This is probably the cause for much of the confusion around this unhelpful term: people imagine that “herd immunity” will make the disease disappear — it won't, it will just stabilize it, and it can stay forever in an endemic state. •13/14

The subthread quoted below is an interesting example of what we call in French a “dialogue de sourds” (“dialogue of the deaf”) whose confusion can only be blamed on how confusing the phrase “herd immunity” is. Maybe it's best avoided entirely. •14/14

https://twitter.com/gro_tsen/status/1316349808836251649