(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
Wolbachia are maternally transmitted endosymbiotic bacteria. To investigate the effect of Wolbachia on the spreading and vanishing of West Nile virus, we construct a reaction-diffusion model associated with the Wolbachia parameter in a heterogeneous environment, which has nonlinear infectious disease parameters. Based on the spectral radius of next infection operator and the related eigenvalue problem, we present a corresponding explicit expression describing the basic reproduction number. Furthermore, utilizing this number, we not only give out the stability of disease-free equilibrium, but also analyze the uniqueness and globally asymptotic behavior of endemic equilibrium. Our theoretical results and numerical simulations indicate that only if Wolbachia reach a certain magnitude in mosquitoes, it can be effective in the control of West Nile virus.