The diffusive SIS epidemic model with mass action infection mechanism on an evolving domain

In this paper, we investigate a diffusive susceptible-infected-susceptible (SIS) epidemic model with a mass action infection mechanism on an evolving domain. The model incorporates logistic population growth for susceptible individuals and the evolution of the time-varying domain is governed by a scaling function ρ(t). We establish the global existence and uniform boundedness of the system. Furthermore, we define the basic reproduction number R0, which relies on the evolution rate of the domain, the diffusion coefficient of the infected populations, etc. We show that the disease-free equilibrium (DFE) is globally stable if R0 < 1, whereas an endemic equilibrium (EE) exists and is globally stable for R0 > 1 in homogeneous environments. We also analyze the asymptotic profiles of the EE for large and small diffusion rates of the susceptible and infected populations. Our numerical simulations indicate that evolving domain is not conducive to the elimination of disease compared to that in fixed domain.