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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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Title: COVID-19 cases and deaths in the United States follow Taylor's law for heavy-tailed distributions with infinite variance.
Authors: Cohen, Joel E.1,2,3,4 cohen@rockefeller.edu, Davis, Richard A.3, Samorodnitsky, Gennady5
Source: Proceedings of the National Academy of Sciences of the United States of America. 9/20/2022, Vol. 119 Issue 38, p1-10. 21p.
Subjects: SARS-CoV-2, COVID-19 pandemic
Geographic Terms: United States
Abstract: The spatial and temporal patterns of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases and COVID-19 deaths in the United States are poorly understood. We show that variations in the cumulative reported cases and deaths by county, state, and date exemplify Taylor's law of fluctuation scaling. 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 lower 99% of counts of cases and deaths across all counties are approximately lognormally distributed. Unexpectedly, the largest 1% of counts are approximately Pareto distributed, with a tail index that implies a finite mean and an infinite variance. We explain why the counts across the entire distribution conform to Taylor's law with exponent two using models and mathematics. The finding of infinite variance has practical consequences. Local jurisdictions (counties, states, and countries) that are planning for prevention and care of largely unvaccinated populations should anticipate the rare but extremely high counts of cases and deaths that occur in distributions with infinite variance. Jurisdictions should prepare collaborative responses across boundaries, because extremely high local counts of cases and deaths may vary beyond the resources of any local jurisdiction. [ABSTRACT FROM AUTHOR]
Copyright of Proceedings of the National Academy of Sciences of the United States of America is the property of National Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: COVID-19 cases and deaths in the United States follow Taylor's law for heavy-tailed distributions with infinite variance.
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  Data: The spatial and temporal patterns of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases and COVID-19 deaths in the United States are poorly understood. We show that variations in the cumulative reported cases and deaths by county, state, and date exemplify Taylor's law of fluctuation scaling. 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 lower 99% of counts of cases and deaths across all counties are approximately lognormally distributed. Unexpectedly, the largest 1% of counts are approximately Pareto distributed, with a tail index that implies a finite mean and an infinite variance. We explain why the counts across the entire distribution conform to Taylor's law with exponent two using models and mathematics. The finding of infinite variance has practical consequences. Local jurisdictions (counties, states, and countries) that are planning for prevention and care of largely unvaccinated populations should anticipate the rare but extremely high counts of cases and deaths that occur in distributions with infinite variance. Jurisdictions should prepare collaborative responses across boundaries, because extremely high local counts of cases and deaths may vary beyond the resources of any local jurisdiction. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Proceedings of the National Academy of Sciences of the United States of America is the property of National Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1073/pnas.2209234119
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              Text: 9/20/2022
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