Metapopulation network models for understanding, predicting and managing the coronavirus disease COVID-19

Calvetti, Daniela; Hoover, Alexander; Rose, Johnie; Somersalo, Erkki

Mathematical models of SARS-CoV-2 spread are used for guiding the design of mitigation steps aimed at containing and decelerating the contagion, and at identifying impending breaches of health care system surge capacity. The challenges of having only lacunary information about daily new infections are compounded by the geographic heterogeneity of the population. To address this problem, we propose to 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 SEIR models. The setting of the model parameters takes into account the fact that SARS-CoV-2 transmission occurs mostly via human-to-human contact, and that the frequency of contact among individuals differs between urban and rural areas, and may change over time. Moreover, the probability that the virus spreads into an uninfected community is associated with influx of individuals from other communities where the infection is present. To account for these important aspects, each node of the network is characterized by the frequency of contact between its members and by its level of connectivity with other nodes. Census and cell phone data can be used to set up the adjacency matrix of the network, which can, in turn, be modified to account for different levels of mitigation measures. In order to make the network SEIR model that we propose easy to customize, it is formulated in terms of easily interpretable parameters that can be estimated from available community level data. The models parameters are estimated with Bayesian techniques using COVID-19 data for the states of Ohio and Michigan. The network model also gives rise to a geographically distributed computational model that explains the geographic dynamics of the contagion, e.g., in larger cities surrounded by suburban and rural areas.