Math of covid-19

The rate at which microbes multiply is proportional to the microbes present at a given time, provided other factors like nutrients and temperature remain favorable.

This equation has the exponential solution . Spread of infections can also be modeled along similar lines, since the rate at which people become infected is expected to be proportional to people already infected.

Interestingly Nicolas Vandevalle has made a model to fit the covid-19 data for Belgium to an exponential curve.

1/ New model SEIR for #covid-19 #coronavirus for determining ICU beds in #Belgium. R0 and other parameters fixed by cases data, while a single free parameter (rescale official data) is used to determine ICU beds. Worst scenario (red curve) and optimistic one (blue curve). pic.twitter.com/0vj9aCfBQ0

— Nicolas Vandewalle (@vdwnico) March 18, 2020

As can be seen, the initial cases of infection follow an exponential curve to a very good approximation, however as the effect of social distancing comes into play, it is possible that the curve may become linear. The data was analyzed for Belgium. Right now, the data is insufficient to say if the curve is turning linear, but the implications are far-reaching.