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

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  • Beare, Brendan K
  • Toda, Alexis Akira

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.

Suggested Citation

  • Beare, Brendan K & Toda, Alexis Akira, 2020. "On the emergence of a power law in the distribution of COVID-19 cases," University of California at San Diego, Economics Working Paper Series qt9k5027d0, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt9k5027d0
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    2. Sk, Tahajuddin & Biswas, Santosh & Sardar, Tridip, 2022. "The impact of a power law-induced memory effect on the SARS-CoV-2 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Yekaterina S Pavlova & David Paez-Espino & Andrew Yu Morozov & Ilya S Belalov, 2021. "Searching for fat tails in CRISPR-Cas systems: Data analysis and mathematical modeling," PLOS Computational Biology, Public Library of Science, vol. 17(3), pages 1-21, March.
    4. Brendan K. Beare & Alexis Akira Toda, 2022. "Determination of Pareto Exponents in Economic Models Driven by Markov Multiplicative Processes," Econometrica, Econometric Society, vol. 90(4), pages 1811-1833, July.
    5. Nick James, 2021. "Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19," Papers 2101.00576, arXiv.org, revised Feb 2021.
    6. Davis, Richard & Ng, Serena, 2023. "Time series estimation of the dynamic effects of disaster-type shocks," Journal of Econometrics, Elsevier, vol. 235(1), pages 180-201.
    7. Nick James & Max Menzies, 2021. "Efficiency of communities and financial markets during the 2020 pandemic," Papers 2104.02318, arXiv.org, revised Jul 2021.
    8. James, Nick, 2021. "Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    9. Kim Chol-jun, 2023. "Distribution in the Geometrically Growing System and Its Evolution," Papers 2302.13781, arXiv.org.

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