>>13838485Sure. I’m defining herd immunity as an effective reproductive number (Re) below 1. That means that without any change, the virus will burn itself out on its own. Re is a function of basic reproductive number (R0; the infectiousness of the virus), and the proportion of people susceptible to infection (S).
Re = R0 * S
where S is further defined as a function of the proportion of the population that is vaccinated (X), and vaccine efficiency (Ve) such that:
S = 1-X*Ve
For the delta variant, R0 = ~5 and Ve is 0.8 for two doses of an mRNA vaccine. So all we need to do is solve for X:
R0 * (1-X*Ve) < 1, which gives ~0.84.
So in other words, with roughly 84 percent of the population twice vaccinated, the virus cannot spread exponentially anymore and infection rates die out.
Now by applying a booster we bring Ve up to ~95 (i.e. comparable to the alpha variant), and solve for X again. This gives ~0.81. So a booster campaign that involves every single person who’s also received the initial two doses only results in a reduction of the herd immunity threshold of 3%. It's a nice bonus, but it's rather on the low side. But as I mentioned, it’s not the main purpose of boosters.
By contrast, changing the X part of the equation (the proportion of people who remain not not yet twice vaccinated), has a much larger impact on Re (the rate of community transmission). This is the reason why scientists hammer on the importance of people getting vaccinated in the first place. A booster is good for staying protected for longer. The initial doses are what matter most for community transmission.
