Metapopulation Network Models for Understanding, Predicting, and Managing the Coronavirus Disease COVID-19

Abstract

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.