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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 US counties and provide prima facie evidence that it follows a power-law over five orders of magnitude. We are able to explain the origin of this scaling behavior by the superposition of two concurrent processes: 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 pandemic. By combining real world data, modeling, and numerical simulations we make the case that that the distribution of epidemic prevalence, and possibly that of spreading processes in general, might follow universal rules.

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