COVID-19 cases fit power-law distribution during initial phase of pandemic

While recent studies have investigated the temporal behavior of COVID-19, little is known about the spatial distribution of cases. Examining the distribution of COVID-19 cases and deaths for countries worldwide and counties in the United States, Bernd Blasius found both distributions follow a truncated power-law distribution over five orders of magnitude during the initial phase of the pandemic.

With a model, the author demonstrated the power-law distributions are a product of two simultaneous processes: the large-scale growth of cases between countries or counties and the small-scale growth of cases in each country or county. Crucially, the critical exponent of the power law can be easily inferred as the ratio of large-scale to small-scale growth rates, assuming exponential growth for both.

This work explains why, during the initial phase of the outbreak, most COVID-19 cases occurred in a few epicenters, while less-affected areas had fewer cases. The disparity in reported cases illustrates the geographical distribution of COVID-19 cases as a power law.

“By combining real-world data, modeling, and numerical simulations, I make the case that the distribution of epidemic prevalence might follow universal rules,” Blasius said. “The model’s strong simplicity is, at the same time, a strength. Being rather generic, it should be applicable to very different systems, indicating that the emergence of a power-law distribution is a natural outcome of the spreading process itself.”

Blasius cautioned a second, post-lockdown wave of COVID-19 may stray from a power-law distribution. Instead, case numbers could simultaneously increase in many places.

“The long tail of the case distribution in the initial phase, characterized by the many regions with only mild epidemic prevalence, could create a false sense of security,” Blasius said.

Source: “Power-law distribution in the number of confirmed COVID-19 cases,” by Bernd Blasius, Chaos (2020). The article can be accessed at https://doi.org/10.1063/5.0013031 .