Department of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, NJ 07102.
Nicholas School of the Environment, Duke University, Durham, NC 27710.
Proc Natl Acad Sci U S A. 2021 May 25;118(21). doi: 10.1073/pnas.2023321118.
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.
新冠病毒感染的时空模式是个人、社会和政治决策的嵌套结果，这些决策涉及到跨越重叠空间尺度的复杂流行病学动态。在疫情早期，高感染“热点”散布在感染仍呈零星分布的地区内，但感染的空间特征逐渐发展为同等程度地影响大多数地区，尽管存在不同的时间模式。美国新冠病毒感染的稀疏性在从 10 到 2600 公里（县到大陆尺度）的多个尺度上进行了分析。美国新冠病例的空间演变遵循多重分形标度。在疫情早期（3 月至 4 月）发现了空间相关性的快速增加。然后，这种增加以较慢的速度继续，并接近人口的空间相关性。本研究提出了一种核调制的易感-感染-恢复（SIR）模型，用于描述多相新冠病毒流行病的传播，该模型不需要跟踪个体，而是采用核调制方法来描述在多分形分布的易感人群中疾病的动态传播。所提出的核调制 SIR 模型合理地再现了多阶段新冠病毒流行病。这项工作解释了这样一个事实，即尽管非药物干预（如口罩、社交距离等）降低了繁殖数，但随后仍会发生多次疫情浪潮；这是由于旅行限制放松和相应的居家令导致易感人群流动增加所致。这项研究对新冠病毒的传播提供了一个原始的解释，并提出了一种实用的方法，可以立即用于捕捉所有具有流行病学意义的尺度上的空间间歇性，同时保留传染性病例的“无序”空间模式。
