Power-law distribution in the number of confirmed COVID-19 cases

COVID-19 is an emerging respiratory infectious disease caused by the coronavirus SARS-CoV-2. It was first reported on in early December 2019 in Wuhan, China and within three month spread as a pandemic around the whole globe. Here, we study macro-epidemiological patterns along the time course of the pandemic. We compute the distribution of confirmed COVID-19 cases and deaths for countries worldwide and for counties in the US, and show that both distributions follow a truncated power-law over five orders of magnitude. We are able to explain the origin of this scaling behavior as a dual-scale process: the large-scale spread of the virus between countries and the small-scale accumulation of case numbers within each country. Assuming exponential growth on both scales, the critical exponent of the power-law is determined by the ratio of large-scale to small-scale growth rates. We confirm this theory in numerical simulations in a simple meta-population model, describing the epidemic spread in a network of interconnected countries. Our theory gives a mechanistic explanation why most COVID-19 cases occurred within a few epicenters, at least in the initial phase of the outbreak. Assessing how well a simple dual-scale model predicts the early spread of epidemics, despite the huge contrasts between countries, could help identify critical temporal and spatial scales of response in which to mitigate future epidemic threats.