Maths musings in COVID times

It was about April 2020, a month into the pandemic. Wear a mask, try to stay largely at home, keep my social distance from people: these were the mantras and priorities for me and for those close to me. Just as they must have been for many others the world over, as we tried to ward off this virus whose spread had already reached frightening proportions.

But while being conscientious about doing those things, there was a sort of meta-me that I was very conscious of. This alter-ego considered the pandemic a huge bonanza for science. In how it opened up all manner of scientific research – for mathematicians and biologists, statisticians and epidemiologists, doctors and chemists, and more. And in that sense, this time of COVID seemed to throw up something new, fascinating and thought-provoking almost daily. True, the dread of the virus loomed over it all. But in the quiet moments, there was space and time to appreciate these other aspects.

Like in April last year. I had already heard plenty about the well-known 'SIR' epidemiological model of pandemics. While it goes back many decades, its simplicity and intuitive feeling are the reasons it stays relevant with every new pandemic, helping us understand its spread.

In its simplest form, this is how SIR works. The population at risk from the virus is divided into three categories: 'Susceptible', 'Infected' and 'Recovered' (thus 'SIR'). Of course, at the start of a pandemic, everyone is susceptible and nobody has either been infected or recovered. But as time goes by, more and more people get infected, thus moving from the 'Susceptible' to the 'Infected' category. As more time goes by, some of those infected recover, moving to 'Recovered'. And, of course, when the pandemic has run its course, pretty much nobody is getting infected any more. Pretty much everyone who was 'Infected' has 'Recovered'.