论文标题
时空空间中确认的COVID-19案件和死亡的重型分布
Heavy-tailed distributions of confirmed COVID-19 cases and deaths in spatiotemporal space
论文作者
论文摘要
本文对累积和每日的地理经验分布的特征进行了系统的统计分析，该累积和每日的数量在2020年1月至2022年6月的一个时间范围内，在县，市和州的案例和死亡中确认了COVID-19案件和死亡。数学重型分布可用于在不同的临时量表和地理量表中拟合经验分布。使用广义帕累托分布对尾部分布的形状参数的估计也支持重型分布的观察。根据重尾分布的特征，地理经验分布的演化过程可以分为三个不同的阶段，即幂律相，lognormal stormal阶段I和对数正态阶段II。这三个阶段可以作为一个区域内Covid-19的严重程度的指标。经验结果表明，人类感染性病毒扩散在人类相互联系的物理复合网络中的重要内在动力学。这些发现扩展了以前的经验研究，可以根据复杂网络理论为当前的数学和物理建模研究提供更严格的限制，例如SIR模型及其变体。
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.
