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Your handy reminder about how herd immunity works. Let's say a single infected person in a fully susceptible population would infect R0 other people on average. Now if a proportion v of the population is immunised then R0*v of those potential infections don't happen (1/n)
and so we only get R0*(1-v) new cases. If R0*(1-v) > 1 then the first case infects more than one other person. Each of those secondary cases also infects more than one other person and so on. We have an outbreak on our hands
If R0*(1-v) < 1 then the first case, on average, infects less than one other person. If they do, by chance happen to infect one or two others, then those secondary cases will also, on average, infect less than one other person and the disease will peter out
So to make sure the disease peters out we need R0*(1-v) to be less than 1, which is the same thing as saying v > 1 - 1/R0. We need enough of the population to be immunised to make sure the disease can’t take hold
For a disease like measles which is highly infectious, R0 is estimated to be between 12 and 18. That means without vaccines, every one of those measles cases would infect 12-18 other people. And for herd immunity we need a minimum of 91-94% of the population to be immunised.
Since some of the population is unable to get vaccinated (mainly young children), those people are completely reliant on the rest of us to do the right thing. Here’s a link again to the CDHB website for official advice cdhb.health.nz/media-release/…
