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.

Covid-19感染的时空格局是嵌套的个人，社会和政治决策的结果，其中涉及跨重叠的空间尺度的复杂流行病学动态。高发感染的“热点”散布在散发感染的区域内，在疫情爆发初期很普遍，但感染的空间特征演变成对大多数区域均等地产生影响，尽管具有不同的时间模式。在美国，Covid-19感染的稀疏性范围为10到2,600 km（县到大陆范围）。在美国，Covid-19病例的空间演变遵循多重分形标度。在疫情爆发的早期（3月至4月），人们发现空间相关性迅速增加。然后，增长继续以较慢的速度进行，并接近人口的空间相关性。代替采用需要跟踪个体的基于代理的模型，开发了一种核调制方法来表征多分形分布易感人群中疾病的动态传播。多阶段Covid-19流行病已通过拟议的内核调制易感性-传染性恢复（SIR）模型得到了合理再现。这项工作解释了这样一个事实：尽管由于非药物干预（例如口罩，社交疏远等）减少了繁殖次数，但随后仍发生了多次流行病。这是由于放宽旅行限制和随之而来的居家定单后易感人群的增加。