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

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.

Economic microbiology: exploring microbes as agents in economic systems

“…However, in diseased states, this balance might be disrupted, leading to a disproportionate distribution of resources and an altered microbial composition, which could contribute to or signify disease. For example, in the field of infectious diseases, heterogeneity in transmission, which represents a challenge for infectious disease dynamics and control, can be modeled according to the 80/20 rule, which has been confirmed for a range of communicable diseases, ranging from influenza to malaria and the recent “Coronavirus Disease 2019” (COVID-19) outbreak ( Woolhouse et al, 1997 ; Chen et al, 2015 ; Cooper et al, 2019 ; Liu and Zheng, 2023 ).…”