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COVID-19 cases and deaths in the United States follow Taylor’s law for heavy-tailed distributions with infinite variance

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Significance Variations in the cumulative reported SARS-CoV-2 cases and COVID-19 deaths by US county, state, and date exemplify Taylor’s law of fluctuation scaling, a widespread ecological and epidemiological pattern. Specifically,… Click to show full abstract

Significance Variations in the cumulative reported SARS-CoV-2 cases and COVID-19 deaths by US county, state, and date exemplify Taylor’s law of fluctuation scaling, a widespread ecological and epidemiological pattern. Specifically, on day 1 of each month from April 2020 through June 2021, each state’s variance (across its counties) of cases is nearly proportional to its squared mean of cases. COVID-19 deaths behave similarly. The largest 1% of counts are approximately Pareto distributed, with a finite mean and an infinite variance. Finding infinite variance has practical consequences. Local jurisdictions (counties, states, and countries) that plan for prevention and care of largely unvaccinated people should anticipate rare but extremely high counts of cases and deaths, by preparing collaborative responses across boundaries.

Keywords: cases deaths; taylor law; variance; infinite variance; united states

Journal Title: Proceedings of the National Academy of Sciences of the United States of America
Year Published: 2022

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