Bull Math Biol https://doi.org/10.1007/s11538-018-0404-8 ORIGINAL ARTICLE Two-patch model for the spread of West Nile virus Juping Zhang 1,2,3 · Chris Cosner 4 · Huaiping Zhu 2 Received: 5 August 2017 / Accepted: 9 February 2018 © Society for Mathematical Biology 2018 Abstract A two-patch model for the spread of West Nile virus between two discrete geographic regions is established to incorporate a mobility process which describes how contact transmission occurs between individuals from and between two regions. In the mobility process, we assume that the host birds can migrate between regions, but not the mosquitoes. The basic reproduction number R 0 is computed by the next generation matrix method. We prove that if R 0 < 1, then the disease-free equilibrium is globally asymptotically stable. If R 0 > 1, the endemic equilibrium is globally asymptotically stable for any nonnegative nontrivial initial data. Using the perturbation theory, we obtain the concrete expression of the endemic equilibrium of the model with a mild restriction of the birds movement rate between patches. Finally, numerical simulations demonstrate that the disease becomes endemic in both patches when birds move back and forth between the two regions. Some numerical simulations for R 0 in terms of the birds movement rate are performed which show that the impacts could be very complicated. This work is partially supported by NSERC and CIHR of Canada, the National Natural Sciences Foundation of China (11331009, 11301491, 11501339), Shanxi Scholarship Council of China (2014-020), the One Hundred Talents Project of Shanxi Province. B Huaiping Zhu huaiping@mathstat.yorku.ca 1 Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China 2 LAMPS and Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada 3 Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006, China 4 Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA 123