Dynamics of West Nile virus driven by seasonal fluctuations in a spatially variable habitat

Abstract

<p style='text-indent:20px;'>Seasonality is the common phenomena in ecological evolution. Firstly, we formulate and explore a simplified West Nile virus model, which describes the transmission of West Nile virus driven by seasonal fluctuations in a spatially variable habitat where the spatial movement of the infectious mosquitoes and infectious birds are described by Laplace diffusion. The range of the infected area is assumed to be a moving interval <inline-formula><tex-math id="M5">\begin{document}$ [0, h(t)] \subset \mathbb{R} $\end{document}</tex-math></inline-formula>, with its right end point representing the spreading fronts of the disease. We will mainly investigate the impact of spatial heterogeneity of environment and temporal periodicity on the persistence and extinction of West Nile virus. The basic reproduction number <inline-formula><tex-math id="M6">\begin{document}$ R_0^D $\end{document}</tex-math></inline-formula> in a fixed region and the spatial-temporal risk index <inline-formula><tex-math id="M7">\begin{document}$ R_0^F(t) $\end{document}</tex-math></inline-formula> for the free boundary problem, which depends on spatial heterogeneity, temporal periodicity and spatial diffusion, are defined by the associated linearized eigenvalue problems. Sufficient conditions for the spreading and vanishing of West Nile virus are presented for the spatial dynamics of the virus. At last, we explore the long time dynamical behavior of the solution to free boundary problem when the spreading occurs.</p>