Variation in R

Variation in R can have a big effect:

While herd immunity is expected to require 60-70% of a homogeneous population to be immune given an R0 between 2.5 and 3, these percentages drop tothe range 10-20% for CVs [coefficient of variation] between 2 and 4.Therefore, a critically importantquestion is: how variable are humans in 120their susceptibility and exposure to SARS-CoV-2?

With this accompanying graph:

This GitHub project shows something similar, with code:

Comparing the two models, the hands-off scenario without lockdown has fewer eventual infections (53% of the population instead of 70%) and the well-timed lockdown scenario still leads to about 20% of the population getting eventually infected.

The point is that R=2.5 is an average. But most people have R closer to 1 and there are a relatively small number of super spreaders with very high R who bring the average up to 2.5.

But an important detail is that super spreaders are not random. While some of it might be biological, much of it is in the size of their social network (think a politician or actor who meets a lot of people). To the extent that’s the case, super spreaders are over-represented among people who get the virus early (if you talk to 1000 people, you’re way more likely to get the virus than if you talk to 10).

If they are over-represented early they must be under-represented later in the pandemic. This means that the initial R0 will drop naturally as fewer super spreaders remain in the susceptible population.

Edit 2020/05/10: this post makes the same point.

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