Asymptotic periodicity in a diffusive West Nile virus model in a heterogeneous environment

This paper is concerned with a diffusive West Nile virus model (WNv) in a heterogeneous environment. The basic reproduction number [Formula: see text] for spatially homogeneous model is first introduced. We then define a threshold parameter [Formula: see text] for the corresponding diffusive WNv model in a heterogeneous environment. It is shown that if [Formula: see text], the model admits at least one nontrivial T-periodic solution, whereas if [Formula: see text], the model has no nontrivial T-periodic solution. By means of monotone iterative schemes, the true solution can be obtained and the asymptotic behavior of periodic solutions is presented. The paper is closed with some numerical simulations to illustrate our theoretical results.