Herd immunity

It's pretty easy to see that the number of people that a given infectious person infects is the product of1

  • the number of people they meet while infectious;
  • the proportion of those people who are not immune;
  • the chance of infecting each person.

As the proportion if people who are immune goes up this number decreases, ultimately to below 1at which point the epidemic dies out more-or-less quickly: this is herd immunity.

If this number is initially around 2, then herd immunity requires about half of the population to be immune. If immunity comes from having had the disease, and the mortality rate is 1%, then about 0.5% of the population need to die to achieve herd immunity. For the UK this means around 350,000 deaths.

The people pushing herd immunity in the early days of the CV19 epidemic were either not numerate enough to realise this or thought that 350,000 deaths was an acceptable price to pay. Clearly Cummings meets both criteria: as a psychopath he doesn't care if hundreds of thousands of other people die, and as an innumerate crank he can't do the maths anyway. But there were other people – apparently real scientists rather than pretend ones like Cummings – who also pushed this idea. If the lack of basic numeracy these people demonstrated dies not terrify you, then it should.

  1. Really it is more complicated, because the chance of infection might depend both on the infecter, the infectee, details of the meeting, the time since the infecter was infected and so on: however I am assuming that these factors are held constant, since all I want to think about is the difference that the proportion of people who are immune or not immune makes.  

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