The role of permanently resident populations in the two-patches SIR model with commuters

TL;DR

This paper analyzes a two-patches SIR model incorporating permanently resident and commuting populations, deriving an explicit reproduction number formula and revealing counterintuitive effects of commuting on epidemic thresholds.

Contribution

It introduces a novel explicit formula for the reproduction number considering resident and commuter populations and explores how commuting impacts epidemic dynamics.

Findings

Commuting can reduce the epidemic threshold under certain conditions.

Explicit formula for the reproduction number considering resident and commuter populations.

Counterintuitive effects of commuting on epidemic spread.

Abstract

We consider a two-patches SIR model where communication occurs thru 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 non-intuitive 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.