The Role of Permanently Resident Populations in the Two-Patches SIR Model with Commuters

Alain Rapaport; Ismail Mimouni

doi:10.1007/s11538-022-01111-6

The Role of Permanently Resident Populations in the Two-Patches SIR Model with Commuters

Bull Math Biol. 2022 Dec 4;85(1):3. doi: 10.1007/s11538-022-01111-6.

Authors

Alain Rapaport¹, Ismail Mimouni²

Affiliations

¹ MISTEA, Université Montpellier, INRAE, Institut Agro, place Viala, 34060, Montpellier, France. alain.rapaport@inrae.fr.
² MISTEA, Université Montpellier, INRAE, Institut Agro, place Viala, 34060, Montpellier, France.

Abstract

We consider a two-patches SIR model where communication occurs through commuters, distinguishing explicitly permanently resident populations from commuters populations. We give an explicit formula of the reproduction number and show how the proportions of permanently resident populations impact it. We exhibit nonintuitive situations for which allowing commuting from a safe territory to another one where the transmission rate is higher can reduce the overall epidemic threshold and avoid an outbreak.

Keywords: Commuters; Patches models; Reproduction number; SIR model.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Disease Outbreaks
Epidemics*
Epidemiological Models*
Mathematical Concepts
Models, Biological