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In this paper, we present a discrete-time networked SEIR model using population flow, its derivation, and assumptions under which this model is well defined. We identify properties of the system’s equilibria, namely the healthy states. We show that the set of healthy states is asymptotically stable, and that the value of the equilibria becomes equal across all sub-populations as a result of the network flow model. Furthermore, we explore closed-loop feedback control of the system by limiting flow between sub-populations as a function of the current infected states. These results are illustrated via simulation based on flight traffic between major airports in the United States. We find that a flow restriction strategy combined with a vaccine roll-out significantly reduces the total number of infections over the course of an epidemic, given that the initial flow restriction response is not delayed. 

In this paper we present a deterministic discrete-time networked SEIR model that includes a number of transportation networks, and present assumptions under which it is well defined. We analyze the limiting behavior of the model and present necessary and sufficient conditions for estimating the spreading parameters from data. We illustrate these results via simulation and with real COVID-19 data from the Northeast United States, integrating transportation data into the results. 

The novel coronavirus responsible for COVID-19 was first identified in Hubei Province, China in December, 2019. Within a matter of months the virus had spread and become a global pandemic. In addition to international air travel, local travel (e.g. by passenger car) contributes to the geographic spread of COVID-19. We modify the common susceptible-exposed-infectious-removed (SEIR) virus spread model and investigate the extent to which short-term travel associated with driving influences the spread of the virus. We consider the case study of the US state of Minnesota, and calibrated the proposed model with travel and viral spread data. Using our modified SEIR model that considers local short-term travel, we are able to better explain the virus spread than using the long-term travel SEIR model. Short-term travel associated with driving is predicted to be a significant contributor to the historical and future spread of COVID-19. The calibrated model also predicts the proportion of infections that were detected. We find that if driving trips remain at current levels, a substantial increase in COVID-19 cases may be observed in Minnesota, while decreasing intrastate travel could help contain the virus spread.