Heavy-tailed distributions of confirmed COVID-19 cases and deaths in spatiotemporal space

TL;DR

This study analyzes the heavy-tailed geographical distributions of COVID-19 cases and deaths over time and space, revealing distinct phases that indicate pandemic severity and inform modeling efforts.

Contribution

It identifies and characterizes heavy-tailed distributions in COVID-19 data across different regions and times, extending previous empirical work and aiding in modeling virus spread.

Findings

COVID-19 distributions follow heavy-tailed patterns.

Three distinct phases of distribution evolution identified.

Results support complex network modeling of virus transmission.

Abstract

This paper conducts a systematic statistical analysis of the characteristics of the geographical empirical distributions for the numbers of both cumulative and daily confirmed COVID-19 cases and deaths at county, city, and state levels over a time span from January 2020 to June 2022. The mathematical heavy-tailed distributions can be used for fitting the empirical distributions observed in different temporal stages and geographical scales. The estimations of the shape parameter of the tail distributions using the Generalized Pareto Distribution also support the observations of the heavy-tailed distributions. According to the characteristics of the heavy-tailed distributions, the evolution course of the geographical empirical distributions can be divided into three distinct phases, namely the power-law phase, the lognormal phase I, and the lognormal phase II. These three phases could serve as an indicator of the severity degree of the COVID-19 pandemic within an area. The empirical results suggest important intrinsic dynamics of a human infectious virus spread in the human interconnected physical complex network. The findings extend previous empirical studies and could provide more strict constraints for current mathematical and physical modeling studies, such as the SIR model and its variants based on the theory of complex networks.