Long-time dynamics of an infection age-structure SIR epidemic model with nonlocal diffusion of Neumann type

In this paper we study a nonlocal dispersal susceptible-infected-removed (SIR) epidemic model with Neumann boundary condition, where the spatial movement of individuals is represented by nonlocal diffusion operator, and the density of infected individuals is related to the age of infection. Using the method of characteristics, we convert the system into a set of coupled reaction-diffusion equations and Volterra integral equations. We introduce the basic reproduction number $R_0$ via a compact positive linear operator and demonstrate that when $R_0<1$, the disease-free equilibrium is globally attractive, while if $R_0>1$, the disease exhibits uniform strong persistence. Numerical simulations are also carried out to support our theoretical results.