Dynamics of a Reaction-Diffusion SIS Epidemic Model with a Control Zone

Abstract. In this paper, we investigate a susceptible-infected-susceptible (SIS) reaction-diffusion model with a control zone where new infections do not occur. We introduce a basic reproduction number [Formula: see text] and establish threshold-type results on the global dynamics in terms of [Formula: see text]. In particular, we design the optimal control zone by investigating the influence of the starting point and length of the control zone in a one-dimensional bounded habitat on disease transmission. We also study the asymptotic distribution of the endemic steady state when the diffusion rates of the population are sufficiently small or large. Our analytical results show that the introduction of control zones tends to suppress the persistence of the disease to some extent and that the restriction of the movement of a population yields to the extinction of the disease at least in low-risk areas.