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Volume 8, Number 2, 2018, Pages 443-456                                                                DOI:10.11948/2018.443
Birds movement impact on the transmission of West Nile virus between patches
Juping Zhang,Zhen Jin,Huaiping Zhu
Keywords:West Nile virus, patch model, birds movement, basic reproduction number, stability.
Abstract:
      Spatial heterogeneity plays an important role in the distribution and persistence of many infectious disease. In the paper, a multi-patch model for the spread of West Nile virus among $n$ discrete geographic regions is presented that incorporates a mobility process. In the mobility process, we assume that the birds can move among regions, but not the mosquitoes based on scale-space. We show that the movement of birds between patches is sufficient to maintain disease persistence in patches. We compute the basic reproduction number $R_{0}$. We prove that if $R_{0}<1$, then the disease-free equilibrium of the model is globally asymptotically stable. When $R_{0}>1$, we prove that there exists a unique endemic equilibrium, which is globally asymptotically stable on the biological domain. Finally, numerical simulations demonstrate that the disease becomes endemic in both patches when birds move back and forth between two regions.
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