Abstract
Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two.
Highlights
Since the outbreak of SARS-CoV-2, the virus which causes COVID-19, in Wuhan, China at the end of 2019 and its rapid spread to nearly every country in the world within a few months, there has been great interest in understanding the transmission of the disease and the dynamics of the epidemic to design and implement suitable control and containment measures
Since in the network model the new infections are explained as a convex combination of local and global infections, a significantly lower local infection rate is sufficient to explain the new cases when taking into account the commuting traffic, suggesting that the first peak in Summit county may have been the result of workplace contacts
Metapopulation-based infection models are quintessential for understanding of the infection dynamics in interconnected non-homogenous populations, whether the nonhomogeneity is due to geographical, socioeconomic or demographic variability
Summary
Since the outbreak of SARS-CoV-2, the virus which causes COVID-19, in Wuhan, China at the end of 2019 and its rapid spread to nearly every country in the world within a few months, there has been great interest in understanding the transmission of the disease and the dynamics of the epidemic to design and implement suitable control and containment measures. Mathematics 2021, 9, 1861 a lossless redistribution of a given density in a prescribed way This framework is ideal to describe human mobility in a closed system, in which the population, originally distributed according to the census data into different communities, is temporarily redistributed as described, e.g., by traffic patterns due to daily commute. The urban centers are linked by major highways that determine the commuter traffic, which in turn is encoded in the transport scheme These models, which can be used as templates for studying the traffic-based spread of COVID-19, provide a realistic test bench for the planning of different mitigation scenarios to contain the virus. The capabilities of an extension to a continuous spatially distributed scheme is demonstrated by a simulated model
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