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.

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.