Asymptotic behavior of the principal eigenvalue and the basic reproduction ratio for periodic patch models

被引：0
作者：
Lei Zhang
Xiao-Qiang Zhao
机构：
[1] Harbin Institute of Technology at Weihai,Department of Mathematics
[2] Memorial University of Newfoundland,Department of Mathematics and Statistics
来源：
Science China Mathematics | 2022年 / 65卷
关键词：
asymptotic behavior; periodic systems; patchy environment; basic reproduction ratio; principal eigenvalue; 34D05; 15A18; 92D30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is devoted to the study of the asymptotic behavior of the principal eigenvalue and the basic reproduction ratio associated with periodic population models in a patchy environment for small and large dispersal rates. We first deal with the eigenspace corresponding to the zero eigenvalue of the connectivity matrix. Then we investigate the limiting profile of the principal eigenvalue of an associated periodic eigenvalue problem as the dispersal rate goes to zero and infinity, respectively. We further establish the asymptotic behavior of the basic reproduction ratio in the case of small and large dispersal rates. Finally, we apply these results to a periodic Ross-Macdonald patch model.
引用
收藏
页码：1363 / 1382
页数：19
相关论文
共 62 条
  • [1] Allen L J(2007)Asymptotic profiles of the steady states for an SIS epidemic patch model SIAM J Appl Math 67 1283-1309
  • [2] Bolker B M(2008)Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model Discrete Contin Dyn Syst 21 1-20
  • [3] Lou Y(2006)The epidemic threshold of vector-borne diseases with seasonality J Math Biol 53 421-436
  • [4] Allen L J(2020)Asymptotic profiles of basic reproduction number for epidemic spreading in heterogeneous environment SIAM J Appl Math 80 1247-1271
  • [5] Bolker B M(2020)Asymptotic profiles of the steady states for an SIS epidemic patch model with asymmetric connectivity matrix J Math Biol 80 2327-2361
  • [6] Lou Y(2009)On the principal eigenvalue of linear cooperating elliptic systems with small diffusion J Evol Equ 9 419-428
  • [7] Bacaer N(1990)On the definition and the computation of the basic reproduction ratio J Math Biol 28 365-382
  • [8] Guernaoui S(2019) in models for infectious diseases in heterogeneous populations SIAM J Appl Math 79 1581-1606
  • [9] Chen S(2020)Travel frequency and infectious diseases Proc Amer Math Soc 148 1709-1722
  • [10] Shi J(2014)Fast diffusion inhibits disease outbreaks Discrete Contin Dyn Syst Ser B 19 3133-3145
1234567