Power Law in COVID-19 Cases in China

Ahundjanov, B. B.; Akhundjanov, S. B.; Okhunjanov, B. B.

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 epicenter 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 less than one, and that a random proportionate growth model predicated by Gibrat's law is a plausible explanation for the emergence of the observed power law behavior. This finding is significant because it implies that COVID-19 cases in China is heavy-tailed and disperse, that a few cities account for a disproportionate share of COVID-19 cases, and that the distribution has no finite mean or variance. The power-law distributedness has implications for effective planning and policy design as well as efficient use of government resources.