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.

中文翻译：

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美国的 COVID-19 病例和死亡遵循具有无限方差的重尾分布的泰勒定律

对美国严重急性呼吸系统综合症冠状病毒 2 (SARS-CoV-2) 病例和 COVID-19 死亡的时空模式知之甚少。我们表明，按县、州和日期划分的累计报告病例和死亡人数的变化体现了泰勒波动比例定律。具体来说，从 2020 年 4 月到 2021 年 6 月，每个月的第 1 天，每个州（跨县）的病例方差几乎与其病例的平方平均值成正比。COVID-19 的死亡表现类似。所有县中较低的 99% 的病例数和死亡数大致呈对数正态分布。出乎意料的是，最大的 1% 的计数近似于 Pareto 分布，尾部指数意味着有限均值和无限方差。我们使用模型和数学解释为什么整个分布的计数符合指数二的泰勒定律。无限方差的发现具有实际意义。计划对大部分未接种疫苗的人群进行预防和护理的地方司法管辖区（县、州和国家/地区）应该预见到罕见但极高的病例数和死亡数，这些病例和死亡人数的分布具有无限差异。司法管辖区应准备跨界协作响应，因为当地极高的病例数和死亡人数可能超出任何地方司法管辖区的资源范围。和国家）正在计划对大部分未接种疫苗的人群进行预防和护理，应该预见到罕见但极高的病例数和死亡人数，这些病例和死亡人数的分布具有无限差异。司法管辖区应准备跨界协作响应，因为当地极高的病例数和死亡人数可能超出任何地方司法管辖区的资源范围。和国家）正在计划对大部分未接种疫苗的人群进行预防和护理，应该预见到罕见但极高的病例数和死亡人数，这些病例和死亡人数的分布具有无限差异。司法管辖区应准备跨界协作响应，因为当地极高的病例数和死亡人数可能超出任何地方司法管辖区的资源范围。