The UK’s autumn Covid-19 booster programme is underway, with approximately 26 million people eligible to receive a jab over the next few months.
Today’s puzzle imagines a hypothetical new variant, and asks the solver to think about how it would spread. It was set by Professor Adam Kucharski of the London School of Hygiene and Tropical Medicine, one of the UK’s leading epidemiologists.
A quick recap for those who have forgotten their Covid maths: R is the reproduction number, meaning the average number of infections caused by any infected person.
The riddle of R
Suppose a hypothetical new COVID variant 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 (i.e. R=2). Every person exposed to the virus will get infected unless they have already had it, in which case they are immune.
As more people get infected, immunity builds, which gradually reduces R until the epidemic peaks and declines. By the end of the variant wave, 75% of the population have 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 take a guess before you try to work it out. A quarter of the population dodge the variant, which is quite a large proportion, even though it seems like quite a fast spreading virus. (England’s reproduction number never reached 2 in 2020 or 2021.)
To do the calculation, here’s a handy equation that might be helpful.
R = R0 x S
R0 (R naught) is the basic reproduction number, meaning the reproduction number when everyone is susceptible. S is a number between 0 and 1 representing the proportion of the population susceptible.
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 Rules of Contagion: Why Things Spread – and Why They Stop
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me..
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