Zhao Lin, Wang Zhi-Cheng, Ruan Shigui
School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People's Republic of China.
Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, 730050, Gansu, People's Republic of China.
J Math Biol. 2018 Dec;77(6-7):1871-1915. doi: 10.1007/s00285-018-1227-9. Epub 2018 Mar 21.
Host heterogeneity can be modeled by using multi-group structures in the population. In this paper we investigate the existence and nonexistence of traveling waves of a two-group SIR epidemic model with time delay and constant recruitment and show that the existence of traveling waves is determined by the basic reproduction number [Formula: see text] More specifically, we prove that (i) when the basic reproduction number [Formula: see text] there exists a minimal wave speed [Formula: see text] such that for each [Formula: see text] the system admits a nontrivial traveling wave solution with wave speed c and for [Formula: see text] there exists no nontrivial traveling wave satisfying the system; (ii) when [Formula: see text] the system admits no nontrivial traveling waves. Finally, we present some numerical simulations to show the existence of traveling waves of the system.
宿主异质性可以通过在总体中使用多群体结构来建模。在本文中，我们研究了一个具有时滞和恒定补充的两组SIR传染病模型行波的存在性和不存在性，并表明行波的存在性由基本再生数[公式：见正文]决定。更具体地说，我们证明：（i）当基本再生数[公式：见正文]时，存在一个最小波速[公式：见正文]，使得对于每个[公式：见正文]，系统都有一个波速为c的非平凡行波解，而对于[公式：见正文]，不存在满足该系统的非平凡行波；（ii）当[公式：见正文]时，系统不存在非平凡行波。最后，我们给出了一些数值模拟来展示该系统行波的存在性。
