Mathematical analysis of a vaccination epidemic model with nonlocal diffusion

Abstract

We study the global dynamics of a susceptible‐vaccinated‐infected‐recovered model that incorporates nonlocal diffusion. By identifying the basic reproduction number of the model, we obtain the following threshold‐type results: (i) If , then the epidemic becomes extinct in the sense that the infection‐free equilibrium is globally attractive; (ii) if and the diffusion coefficients are the same for all classes, then the epidemic persists in the sense that the system is uniformly persistent; and (iii) if , the diffusion coefficients for susceptible, and the vaccinated classes are zero, then the system admits a unique endemic equilibrium, and the omega‐limit set is included in the singleton of the endemic equilibrium. Our results show that is an essential value for determining global epidemic dynamics in our model.