Effect of diffusion rates on a nonlocal SIS model with distinct dispersal kernels and logistic source

Abstract

We investigate a nonlocal SIS epidemic model that incorporates distinct mobility patterns for susceptible and infected individuals, together with a logistic growth. The model includes distinct nonlocal diffusion kernels, denoted by J₁(x) and J₂(x), which represent different mobility strategies of the susceptible and infected populations, respectively. This formulation enhances the biological realism of the model by allowing greater flexibility in the representation of individual movement behaviors. Consequently, it introduces additional mathematical challenges in the analysis while providing a more accurate modelling for studying the spatial spread of infectious diseases. We establish the well-posedness, positivity, and uniform boundedness of solutions, and prove the existence of a global attractor. The basic reproduction number $R_0$ is derived, and persistence theory is used to show the existence of an endemic steady state when $R_0>1$. We further analyze the asymptotic profiles of the endemic steady states under extreme diffusion limits, highlighting the impact of mobility on disease persistence.