On the emergence of a power law in the distribution of COVID-19 cases

Brendan Beare and Alexis Akira Toda

University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

Abstract: 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 180,000 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.

Keywords: Applied Mathematics; Mathematical Physics; Numerical and Computational Mathematics; Mathematical Sciences; Coronavirus; COVID-19; Gibrat's law; Mathematical modeling of epidemics; Power law; Tauberian theorem; Gibrat’s law; physics.soc-ph; q-bio.PE; Fluids & Plasmas; Applied mathematics; Mathematical physics; Numerical and computational mathematics (search for similar items in EconPapers)
Date: 2020-11-01
New Economics Papers: this item is included in nep-hme
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Citations: View citations in EconPapers (10)

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