Global dynamics of a West Nile virus model in a spatially variable habitat

In this paper, we investigate a mathematical model that describes the transmission dynamics of West Nile virus (WNV) associated with the mosquito-bird population in a continuous bounded habitat. Our model is given by a spatial reaction-diffusion system with the zero-flux condition on the boundary, which is motivated by the models in the previous works of Wonham et al. (2004) and Lewis et al. (2006). By using the comparison theorem and the theory of uniform persistence, we show that the global dynamics of the model can be determined by two indices, mosquito reproduction number and infection invasion threshold.