Mathematical models of SARS-CoV-2 (the virus which causes COVID-19) spread are used for guiding the design of mitigation steps and helping identify impending breaches of health care system surge capacity. The challenges of having only lacunary information about daily new infections and mortality counts are compounded by geographic heterogeneity of the population. This complicates prediction, particularly when using models assuming well-mixed populations. To address this problem, we account for the differences between rural and urban settings using network-based, distributed models where the spread of the pandemic is described in distinct local cohorts with nested SE(A)IR models, i.e., modified SEIR models that include infectious asymptomatic individuals. The model parameters account for the SARS-CoV-2 transmission mostly via human-to-human contact, and the fact that contact frequency among individuals differs between urban and rural areas, and may change over time. The probability that the virus spreads into an uninfected community is associated with influx of individuals from communities where the infection is already present, thus each node is characterized by its internal contact and by its connectivity with other nodes. Census data are used to set up the adjacency matrix of the network, which can be modified to simulate changes in mitigation measures. Our network SE(A)IR model depends on easily interpretable parameters estimated from available community level data. The parameters estimated with Bayesian techniques include transmission rate and the ratio asymptomatic to symptomatic infectious individuals. The methodology predicts that the latter quantity approaches 0.5 as the epidemic reaches an equilibrium, in full agreement with the May 22, 2020 CDC modeling. The network model gives rise to a spatially distributed computational model that explains the geographic dynamics of the contagion, e.g., in larger cities surrounded by suburban and rural areas. The time courses of the infected cohorts in the different counties predicted by the network model are remarkably similar to the reported observations. Moreover, the model shows that monitoring the infection prevalence in each county, and adopting local mitigation measures as infections climb beyond a certain threshold, is almost as effective as blanket measures, and more effective than reducing inter-county mobility.

SARS-CoV-2（引起COVID-19的病毒）传播的数学模型可用于指导缓解措施的设计，并帮助识别即将发生的违反医疗保健系统喘振能力的情况。仅拥有有关日常新感染和死亡率计数的基础信息的挑战因人口的地理异质性而更加复杂。这使预测变得复杂，尤其是在使用假设人口充分混合的模型时。为了解决此问题，我们使用基于网络的分布式模型解决了农村和城市环境之间的差异，其中在不同的本地队列中使用嵌套的SE（A）IR模型描述了大流行的蔓延，即，修改后的SEIR模型包括传染性无症状个体。模型参数主要通过人与人之间的接触来解释SARS-CoV-2的传播，个体之间的接触频率在城乡之间有所不同，并且可能随时间而变化。病毒传播到未感染社区的可能性与已经存在感染的社区的个体涌入有关，因此每个节点的特征在于其内部接触以及与其他节点的连通性。人口普查数据用于建立网络的邻接矩阵，可以对其进行修改以模拟缓解措施的变化。我们的网络SE（A）IR模型取决于根据可用社区级别数据估算的易于解释的参数。用贝叶斯技术估计的参数包括传播速度和无症状感染者与有症状感染者的比率。该方法预测后一个数量接近0。与流行病达到平衡时的5完全符合2020年5月22日疾病预防控制中心的模型。网络模型产生了一个空间分布的计算模型，该模型解释了传染病的地理动态，例如在郊区和农村包围的大城市中。网络模型预测的不同县的受感染人群的时间进程与报告的观察结果非常相似。此外，该模型显示，监控每个县的感染率，并在感染量超过一定阈值时采取局部缓解措施，几乎与全面措施一样有效，并且比减少县际流动性更有效。网络模型产生了一个空间分布的计算模型，该模型解释了传染病的地理动态，例如在郊区和农村包围的大城市中。网络模型预测的不同县的受感染人群的时间进程与报告的观察结果非常相似。此外，该模型显示，监控每个县的感染率，并在感染量超过一定阈值时采取局部缓解措施，几乎与全面措施一样有效，并且比减少县际流动性更有效。网络模型产生了一个空间分布的计算模型，该模型解释了传染病的地理动态，例如在郊区和农村包围的大城市中。网络模型预测的不同县的受感染人群的时间进程与报告的观察结果非常相似。此外，该模型显示，监控每个县的感染率，并在感染量超过一定阈值时采取局部缓解措施，几乎与全面措施一样有效，并且比减少县际流动性更有效。网络模型预测的不同县的受感染人群的时间进程与报告的观察结果非常相似。此外，该模型显示，监控每个县的感染率，并在感染量超过一定阈值时采取局部缓解措施，几乎与全面措施一样有效，并且比减少县际流动性更有效。网络模型预测的不同县的受感染人群的时间进程与报告的观察结果非常相似。此外，该模型显示，监控每个县的感染率，并在感染量超过一定阈值时采取局部缓解措施，几乎与全面措施一样有效，并且比减少县际流动性更有效。