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This paper is concerned with a simplified epidemic model for West Nile virusin a heterogeneous time-periodic environment. By means of the model, we willexplore the impact of spatial heterogeneity of environment and temporalperiodicity on the persistence and eradication of West Nile virus. The freeboundary is employed to represent the moving front of the infected region. Thebasic reproduction number $R_0^D$ and the spatial-temporal risk index$R_0^F(t)$, which depend on spatial heterogeneity, temporal periodicity andspatial diffusion, are defined by considering the associated linearizedeigenvalue problem. Sufficient conditions for the spreading and vanishing ofWest Nile virus are presented for the spatial dynamics of the virus.

The spatial-temporal risk index and spreading dynamics for a time-periodic diffusive WNv model