Global proprieties of an SIR epidemic model with nonlocal diffusion and immigration

Immigration is the responsible for transmitting disease from one country to another. In this research, we investigate the global proprieties of an SIR model with nonlocal dispersal and immigration. The main purpose is to show that immigration will eliminate the threshold dynamics known for SIR epidemic models, and leads to the persistence of the disease independently of the parameters. Based on Lipschitz continuity of parameters, it has been shown that the strictly positive equilibrium state exists and it is unique. Using the infected density equilibrium as the integral kernel of a Lyapunov function, we also proved the global attractiveness of the endemic equilibrium state, the mathematical findings are checked numerically.