America was not prepared for the magnitude of the Pandemic. There may have been a mathematical method to the madness of those early days.
A model that closely matches the patterns of case counts and deaths reported in the United States between April 2020 and June 2021 is being tested. Local jurisdictions could be overwhelmed by unprecedented COVID spikes, according to the model.
"Based on the data, our best estimate is that the number of cases and deaths per county have infinite variance, which means that a county could get hit with a tremendous number of cases or deaths," says Rockefeller University'sJoel Cohen. We don't know if any county will have the resources to cope with large, rare events, so it's important that states and countries share resources.
Predicting how many people will get a flu.
Ecologists might have thought that the spread of COVID cases and deaths would conform to Taylor's Law, a formula that relates a population's mean to its deviation. Taylor's Law is the basis of many statistical models used to describe thousands of species.
Cohen ran into a surprise when he looked into whether Taylor's Law could describe the grim statistics provided by the New York Times.
Taylor's Law predicts that the variance of cases or deaths in each location will be proportional to the squared mean of cases. Taylor's Law predicts that the scatter of case counts in California will be four times larger than the scatter of case counts in Arizona if the average number of cases per county is 50. The scatter would be nine times larger in California if the case counts were 50 and 150.
The top one percent of counts did not fit the normal distribution. The high counts matched the Pareto distribution, which is a model more often seen in economics than biology. The Pareto distribution was unique because it had infinite variance and implied that the scatter would increase beyond any finite limit. The top 1% of counts still conformed to Taylor's Law despite the fact that the lower 99% did not.
Cohen says it was a puzzle. I sat on that puzzle and took it out, torturing it a bit, and put it away. I used to call in the heavy artillery.
One percent is left.
Cohen asked Gennady Samorodnitsky of Cornell University and Richard A. Davis of Columbia University for their feedback. There was a missing proof that Taylor's Law would hold for the top 1% of counties.
Cohen says that the theorems helped prove that Taylor's Law is accurate. There was an orderly pattern of deaths and cases during the Pandemic. There was no limit to how bad things could get in the most extreme instances.
Near-infinite trouble.
The hybrid (lognormal-Pareto) version of Taylor's Law is closely followed by the swine flu. Taylor's Law can be used to describe the nature of infectious diseases like Chagas's disease. We would expect the number of cases to increase and the number of people to be changed by random events.
Cohen hopes that the study will make policymakers think twice. An infinite variation of cases and deaths per county means that there is a very unlikely scenario in which a COVID spike gets everyone in that county sick or worse. Although the advent of vaccines makes such a scenario less likely, areas with low vaccination rates still face the possibility of spikes that they can't handle.
Cohen thinks that COVID cases and deaths could far exceed the capacity of local jurisdictions. He says that governments should be prepared to call in their friends.
More information: Joel E. Cohen et al, COVID-19 cases and deaths in the United States follow Taylor's law for heavy-tailed distributions with infinite variance, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.2209234119 Journal information: Proceedings of the National Academy of Sciences
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