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 Modeling the spread of West Nile virus in a spatially heterogeneous and advective environment Jing Ge,Zhigui Lin,Huaiping Zhu Keywords:West Nile virus; heterogeneity; advection; free boundary; the risk index Abstract: In this paper, we put forward and explore a reaction-diffusion-advection system with free boundaries in spatially heterogeneous environment to model the spatial spreading of West Nile virus. The transmission dynamics are given for the model involving mosquitoes and birds, and the free boundaries are introduced to describe the moving fronts of the infected region. The spatial-temporal risk index $R_0^F(t)$ , which depends on time $t$, spatial heterogeneity and advection intensity, is derived by variational method. Sufficient conditions for the virus to extinct or to persist are given. Our results show that, if $R^F_0(\infty)\leq 1$, the virus extinct eventually, and if $R^F_0(t_0)\geq 1$ for some $t_0\geq 0$, the virus will spread continuously, while if \$R^F_0(0)<1