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

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.