On a partially degenerate West Nile virus model in closed advective environments

To gain deeper insights into the impact of bird dispersal and advection on the spread of West Nile virus, this study focuses on a partially degenerate reaction–diffusion model of the virus within closed advective environments with spatial heterogeneity. Initially, we define the basic reproduction number for this model and establish a threshold-type result based on it. Furthermore, we explore properties of the basic reproduction number concerning diffusion and advection rates by analyzing an eigenvalue problem involving weight and potential. The detailed dynamical classifications of such a model are delineated as the diffusion and advection rates vary. Theoretical and numerical results indicate that spatial heterogeneity, diffusion rate, advection rate and recovery rate of birds all significantly impact the survival or extinction of species.