Complex Systems Research Center, Shanxi University, Taiyuan, 030006, Shanxi, China.
LAMPS and Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada.
Bull Math Biol. 2018 Apr;80(4):840-863. doi: 10.1007/s11538-018-0404-8. Epub 2018 Feb 28.
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 [Formula: see text] is computed by the next generation matrix method. We prove that if [Formula: see text], then the disease-free equilibrium is globally asymptotically stable. If [Formula: see text], 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 [Formula: see text] in terms of the birds movement rate are performed which show that the impacts could be very complicated.
建立了一个两补丁模型来描述西尼罗河病毒在两个离散地理区域之间的传播，该模型纳入了一个描述个体在两个区域之间如何发生接触传播的迁移过程。在迁移过程中，我们假设宿主鸟类可以在区域之间迁移，但蚊子不能。基本繁殖数 [公式：见文本] 通过下一代矩阵方法计算。我们证明，如果 [公式：见文本]，则无病平衡点是全局渐近稳定的。如果 [公式：见文本]，则对于任何非负的非平凡初始数据，地方病平衡点都是全局渐近稳定的。利用微扰理论，我们得到了模型在鸟类斑块间迁移率的一个轻微限制下的地方病平衡点的具体表达式。最后，数值模拟表明，当鸟类在两个区域之间来回移动时，疾病在两个斑块中都会成为地方病。还针对 [公式：见文本] 进行了一些关于鸟类迁移率的数值模拟，结果表明影响可能非常复杂。
