A Nonlocal Reaction-Diffusion Model of West Nile Virus with Vertical Transmission

West Nile virus (WNv) is a mosquito-borne infection, causing health challenges to bird and human populations. We propose a general nonlocal reaction-diffusion model to explore the combined effect of alternative hosts, vector-host movement and spatial-temporal environmental structure onWNv transmission dynamics. The model is partially degenerate and its solution maps lack compactness due to the absence of diffusion terms in larval equations. For this tightly coupled disease model, we introduce the mosquito reproduction number R-0(V) and WNv reproduction number R-0, respectively, and further show that these two aforementioned reproduction numbers completely determine the threshold behavior of the disease spread. Numerical simulations support our analytic results and suggest that environmental heterogeneity plays an important role in shaping WNv dynamics. Moreover, bird migration may increase the disease risk.