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We consider a two-patches SIR model where communication occurs thrucommuters, distinguishing explicitly permanently resident populations fromcommuters populations. We give an explicit formula of the reproduction number,and show how the proportions of permanently resident populations impact it. Weexhibit non-intuitive situations for which allowing commuting from a safeterritory to another one where the transmission rate is higher can reduce theoverall epidemic threshold and avoid an outbreak.

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