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. I. INTRODUCTIONGlobal interconnectivity has proven to be a key factor in the propagation of infectious diseases [1], [2]. Most recently, we have seen evidence of such connectivity through the rapid spread of the COVID-19 pandemic, which propagated from its origin in Wuhan, China to every major population center globally in a matter of weeks [3]. Given the implications of global population flow on disease spread, it becomes important to accurately model this flow, as reliable modeling is an essential step to developing effective and efficient mitigation strategies. Various infection models have been proposed based on characteristics of individual pathogens and studied in the literature, including susceptible-infected-susceptible (SIS), susceptible-infected-removed (SIR), and susceptible-infected-removed-susceptible (SIRS) [4], [5]. For this paper, we consider the recent COVID-19 pandemic as a motivating case for the model selection and construction. Due to the delay in onset of COVID-19 symptoms [6]-[9] and large asymptomatic populations estimated between 17 − 81% [10]-[13], we choose the susceptible-exposed-infected-removed (SEIR) model as the foundation of our model development. Previous work involving the incorporation of population flows in epidemic process models include analysis of a networked SIS model with flows [14] as well as using a networked SIR model with flows to predict arrival times for various epidemics using global flight data [15], where both models are developed in continuous time. This paper uses similar derivation techniques to define our discrete-time epidemic model. However, we contribute to the development of such models by including the exposed state in our model formulation, as well as provide analysis of the discrete time dynamics. While other work has considered capturing the effect of transportation on the spread of COVID-19 using the SEIR model [16], the key distinction in this work is that infection propagation over the network is modeled by the relocation of infected individuals

No abstract