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

Brooks Butler, Ciyuan Zhang, Ian Walter, Nishant Nair, Raphael Stern, Philip E. Pare

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4260-4265
Number of pages6
ISBN (Electronic)9781665436595
DOIs
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: Dec 13 2021Dec 17 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2021-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States
CityAustin
Period12/13/2112/17/21

Bibliographical note

Funding Information:
*Brooks Butler, Ciyuan Zhang, Ian Walter, Nishant Nair, and Philip. E. Paré are with the School of Electrical and Computer Engineering at Purdue University. Emails: {brooksbutler, zhan3375, walteri, nair65, philpare}@purdue.edu. Raphael Stern is with the Department of Civil, Environmental, and Geo-Engineering at the University of Minnesota, Email: {rstern@umn.edu}. This work was funded in part by the C3.ai Digital Transformation Institute sponsored by C3.ai Inc. and the Microsoft Corporation and in part by the National Science Foundation, grants NSF-CNS #2028738 (P.E.P.), NSF-CNS #2028946 (R.S.), and NSF-ECCS #2032258 (P.E.P).

Publisher Copyright:
© 2021 IEEE.

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