Lin Zhigui, Zhu Huaiping
School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China.
Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada.
J Math Biol. 2017 Dec;75(6-7):1381-1409. doi: 10.1007/s00285-017-1124-7. Epub 2017 Apr 4.
In this paper, a reaction-diffusion system is proposed to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America. Transmission dynamics are based on a simplified model involving mosquitoes and birds, and the free boundary is introduced to model and explore the expanding front of the infected region. The spatial-temporal risk index [Formula: see text], which involves regional characteristic and time, is defined for the simplified reaction-diffusion model with the free boundary to compare with other related threshold values, including the usual basic reproduction number [Formula: see text]. Sufficient conditions for the virus to vanish or to spread are given. Our results suggest that the virus will be in a scenario of vanishing if [Formula: see text], and will spread to the whole region if [Formula: see text] for some [Formula: see text], while if [Formula: see text], the spreading or vanishing of the virus depends on the initial number of infected individuals, the area of the infected region, the diffusion rate and other factors. Moreover, some remarks on the basic reproduction numbers and the spreading speeds are presented and compared.
本文提出了一个反应扩散系统，用于模拟西尼罗河病毒在北美媒介蚊子和宿主鸟类中的空间传播。传播动力学基于一个涉及蚊子和鸟类的简化模型，并引入自由边界来模拟和探索感染区域的扩展前沿。针对具有自由边界的简化反应扩散模型，定义了涉及区域特征和时间的时空风险指数[公式：见原文]，以便与其他相关阈值进行比较，包括通常的基本再生数[公式：见原文]。给出了病毒消失或传播的充分条件。我们的结果表明，如果[公式：见原文]，病毒将处于消失的情形；如果对于某个[公式：见原文]，[公式：见原文]，病毒将传播到整个区域；而如果[公式：见原文]，病毒的传播或消失取决于感染个体的初始数量、感染区域的面积、扩散率和其他因素。此外，还给出并比较了关于基本再生数和传播速度的一些说明。
