Wang Zhiguo, Nie Hua, Du Yihong
School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710119, Shaanxi, China.
School of Science and Technology, University of New England, Armidale, NSW, 2351, Australia.
J Math Biol. 2019 Jul;79(2):433-466. doi: 10.1007/s00285-019-01363-2. Epub 2019 Apr 23.
The purpose of this paper is to determine the precise asymptotic spreading speed of the virus for a West Nile virus model with free boundary, introduced recently in Lin and Zhu (J Math Biol 75:1381-1409, 2017), based on a model of Lewis et al. (Bull Math Biol 68:3-23, 2006). We show that this speed is uniquely defined by a semiwave solution associated with the West Nile virus model. To find such a semiwave solution, we firstly consider a general cooperative system over the half-line [Formula: see text], and prove the existence of a monotone solution by an upper and lower solution approach; we then establish the existence and uniqueness of the desired semiwave solution by applying this method together with some other techniques including the sliding method. Our result indicates that the asymptotic spreading speed of the West Nile virus model with free boundary is strictly less than that of the corresponding model in Lewis et al. (2006).
本文的目的是基于Lewis等人（《数学生物学通报》68:3 - 23，2006）的模型，确定Lin和Zhu（《数学生物学杂志》75:1381 - 1409，2017）最近引入的具有自由边界的西尼罗河病毒模型中病毒的确切渐近传播速度。我们表明，这个速度由与西尼罗河病毒模型相关的半波解唯一确定。为了找到这样的半波解，我们首先考虑半直线[公式：见文本]上的一般合作系统，并通过上下解方法证明单调解的存在性；然后通过将此方法与包括滑动方法在内的其他一些技术相结合，建立所需半波解的存在性和唯一性。我们的结果表明，具有自由边界的西尼罗河病毒模型的渐近传播速度严格小于Lewis等人（2006）中相应模型的传播速度。
