Dynamics analysis of a quarantine model in two patches

Abstract

A new deterministic model for assessing the impact of quarantine on the transmission dynamics of a communicable disease in a two‐patch community is designed. Rigorous analysis of the model shows that the imperfect nature of quarantine (in the two patches) could induce the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity. For the case when quarantined susceptible individuals do not acquire infection during quarantine, the disease‐free equilibrium of the model is shown to be globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model has a unique Patch i‐only boundary equilibrium (i = 1,2) whenever the associated reproduction number for Patch i is greater than unity. The unique Patch i‐only boundary equilibrium is locally asymptotically stable whenever the invasion reproduction number of Patch 3 − i is less than unity (and the associated reproduction number for Patch i exceeds unity). The model has at least one endemic equilibrium when its reproduction number exceeds unity (and the disease persists in both patches in this case). It is shown that adding multi‐patch dynamics to a single‐patch quarantine model (which allow the quarantine of susceptible individuals) in a single patch does not alter its quantitative dynamics (with respect to the existence and asymptotic stability of its associated equilibria as well as its backward bifurcation property). Copyright © 2014 John Wiley & Sons, Ltd.