  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.
