Birds movement impact on the transmission of West Nile virus between patches |
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Authors: | Juping Zhang Zhen Jin and Huaiping Zhu |
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Institution: | Complex Systems Research Center, Shanxi University, Taiyuan City, Shanxi Province, 030006, China;Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan City, Shanxi Province, 030006, China,Complex Systems Research Center, Shanxi University, Taiyuan City, Shanxi Province, 030006, China;Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan City, Shanxi Province, 030006, China,Complex Systems Research Center, Shanxi University, Taiyuan City, Shanxi Province, 030006, China;LAMPS and Department of Mathematics and Statistics,York University, Toronto, Ontario, M3J 1P3, Canada |
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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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Keywords: | West Nile virus patch model birds movement basic reproduction number stability |
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