The Effect of Population Flow on Epidemic Spread: Analysis and Control

TL;DR

This paper develops a networked SEIR model incorporating population flow to analyze epidemic spread and proposes flow control strategies that, combined with vaccination, effectively reduce infections.

Contribution

It introduces a discrete-time networked SEIR model with flow control and analyzes its equilibria and stability, providing new insights into epidemic management.

Findings

Flow restrictions combined with vaccination reduce total infections.

Healthy states are asymptotically stable under the model.

Flow control effectiveness depends on timely implementation.

Abstract

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.