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Can you figure it out? A mathematics of a hypothetical new variant of Covid | math

The UK’s autumn Covid-19 booster program is clandestine, with an estimated 26 million people eligible to receive a shot in the coming months.

Today’s puzzle imagines a hypothetical new variant and asks the solver to think about how it would spread. It was established by Professor Adam Kucharski of the London School of Hygiene and Tropical Medicine, one of the UK’s leading epidemiologists.

A quick summary for those who have forgotten their Covid math: R is the reproduction number, i.e. the average number of infections caused by any one infected person.

The puzzle of R

Suppose a hypothetical new variant of COVID emerges and everyone is initially susceptible to infection (but not necessarily severe disease).

During the early stages of this new wave, each infected person exposes the variant to two other people (ie, R=2). All people exposed to the virus will become infected unless they have already had it, in which case they are immune.

As more people become infected, immunity develops, gradually lowering R until the epidemic peaks and subsides. At the end of the variant wave, 75% of the population has been infected with this variant.

On average, how many times was each person in the population exposed to infection during this wave? What is surprising about this result?

You might want to guess before trying to solve it. A quarter of the population dodges the variant, which is a fairly large proportion, although it seems like a fairly fast-spreading virus. (England’s breeding number never reached 2 in 2020 or 2021.)

To do the math, here’s a handy equation that might come in handy.

R = R0 x page

R0 (R zero) is the basic reproduction number, that is, the reproduction number when everyone is susceptible. S is a number between 0 and 1 that represents the proportion of the susceptible population.

I’ll be back at 5pm UK with the answer and a discussion.

PLEASE NO SPOILERS.

Thanks to Adam Kucharski. He is the author of the fantastic. Contagion rules: why things spread and why they stop

I put a puzzle here every two weeks on Mondays. I’m always looking for great puzzles. If you want to suggest one, send me an email.

I give school talks on math and riddles (online and face-to-face). If your school is interested please get in touch.

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