Power law in COVID-19 cases in China.

The novel coronavirus (COVID-19) was first identified in China in December 2019. Within a short period of time, the infectious disease has spread far and wide. This study focuses on the distribution of COVID-19 confirmed cases in China-the original epicentre of the outbreak. We show that the upper tail of COVID-19 cases in Chinese cities is well described by a power law distribution, with exponent around one in the early phases of the outbreak (when the number of cases was growing rapidly) and less than one thereafter. This finding is significant because it implies that (i) COVID-19 cases in China is heavy tailed and disperse; (ii) a few cities account for a disproportionate share of COVID-19 cases; and (iii) the distribution generally has no finite mean or variance. We find that a proportionate random growth model predicated by Gibrat's law offers a plausible explanation for the emergence of a power law in the distribution of COVID-19 cases in Chinese cities in the early phases of the outbreak.