期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2021
卷号：118
期号：21
DOI：10.1073/pnas.2023321118
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Significance
Spatial analysis of daily Covid-19 cases at the US county scale revealed a dynamic multifractal scaling of infections, spanning from 10 to 2,600 km and consistently trending toward that of the susceptible population. A susceptible–infected–recovered model was expanded to include spatial spread across counties using a spatial kernel. The reproduction number
R
b (average number of persons infected by an infected person) decreased because of interventions (masks, social distancing). The model shows that reducing
R
b in isolation is not sufficient to stem the spread of the disease and concomitant measures such as curfews and lockdowns may be needed. The
R
b of 2.0 estimated here in July to October 2020 is large, hinting at super-spreaders and super-spreader events.
The tempo-spatial patterns of Covid-19 infections are a result of nested personal, societal, and political decisions that involve complicated epidemiological dynamics across overlapping spatial scales. High infection “hotspots” interspersed within regions where infections remained sporadic were ubiquitous early in the outbreak, but the spatial signature of the infection evolved to affect most regions equally, albeit with distinct temporal patterns. The sparseness of Covid-19 infections in the United States was analyzed at scales spanning from 10 to 2,600 km (county to continental scale). Spatial evolution of Covid-19 cases in the United States followed multifractal scaling. A rapid increase in the spatial correlation was identified early in the outbreak (March to April). Then, the increase continued at a slower rate and approached the spatial correlation of human population. Instead of adopting agent-based models that require tracking of individuals, a kernel-modulated approach is developed to characterize the dynamic spreading of disease in a multifractal distributed susceptible population. Multiphase Covid-19 epidemics were reasonably reproduced by the proposed kernel-modulated susceptible–infectious–recovered (SIR) model. The work explained the fact that while the reproduction number was reduced due to nonpharmaceutical interventions (e.g., masks, social distancing, etc.), subsequent multiple epidemic waves still occurred; this was due to an increase in susceptible population flow following a relaxation of travel restrictions and corollary stay-at-home orders. This study provides an original interpretation of Covid-19 spread together with a pragmatic approach that can be imminently used to capture the spatial intermittency at all epidemiologically relevant scales while preserving the “disordered” spatial pattern of infectious cases.
