  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.
