THRESHOLD DYNAMICS OF A REACTION-DIFFUSION CHOLERA MODEL WITH SEASONALITY AND NONLOCAL DELAY

In this paper, we investigate the threshold results for a nonlocal and time-delayed reaction-diffusion system involving the spatial heterogeneity and the seasonality. Due to the complexity of the model, we rigorously analyze the well-posedness of the model. The basic reproduction number R-0 is characterized with the next generation operator method. We show that the disease-free omega-periodic solution is globally attractive when R-0 < 1; while the system is uniformly persistent and a positive ! -periodic solution exists when R-0 > 1. In a special case that the parameters are all independent of the spatial heterogeneity and the seasonality, the global attractivity of the constant equilibria of the model is investigated by the technique of Lyapunov functionals.