Dynamics of a spatiotemporal SIS epidemic model with distinct mobility range

Abstract

In this study, we consider an epidemic model for susceptible-infected-susceptible populations with nonlocal dffusion, described by convolution operators. Our main objective is to model different diffusion strategies for the susceptible and infected populations by using distinct kernel functions in the convolution operator to model the different movements of individuals for each class. This approach eliminates the simplification of reducing the stationary problem to a single equation, which makes the analysis more challenging. However, we have shown the existence of at least one positive endemic steady state when the basic reproduction number is greater than one, using the index degree theory of Leray-Schauder. Additionally, we investigated the asymptotic profile of the endemic equilibrium state for both, large and small diffusion rates, to demonstrate the persistence or extinction of the disease. Overall, our study indicates that restricting individual movements only partially cannot eliminate the disease unless the total population size is small.