  The first confirmed case of Coronavirus Disease 2019 (COVID-19) in the US was
reported on January 21, 2020. By the end of March, 2020, there were more than
180000 confirmed cases in the US, distributed across more than 2000 counties.
We find that the right tail of this distribution exhibits a power law, with
Pareto exponent close to one. We investigate whether a simple model of the
growth of COVID-19 cases involving Gibrat's law can explain the emergence of
this power law. The model is calibrated to match (i) the growth rates of
confirmed cases, and (ii) the varying lengths of time during which COVID-19 had
been present within each county. Thus calibrated, the model generates a power
law with Pareto exponent nearly exactly equal to the exponent estimated
directly from the distribution of confirmed cases across counties at the end of
March.
