具有非局部效应的时滞SEIR系统的周期行波解

数学物理学报 ›› 2024, Vol. 44 ›› Issue (1): 140-159.

具有非局部效应的时滞SEIR系统的周期行波解

张广新(),杨赟瑞^*(),宋雪()

兰州交通大学数理学院兰州 730070

收稿日期:2023-02-06 修回日期:2023-08-16 出版日期:2024-02-26 发布日期:2024-01-10
通讯作者: 杨赟瑞, E-mail:lily1979101@163.com
作者简介:张广新, E-mail:z13526096865@163.com|宋雪, E-mail:sx18604126839@163.com
基金资助:
国家自然科学基金(12361038);国家自然科学基金(117610468);甘肃省自然科学基金(20JR5RA411)

Periodic Traveling Wave Solutions of Delayed SEIR Systems with Nonlocal Effects

Zhang Guangxin(),Yang Yunrui(),Song Xue()

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070

Received:2023-02-06 Revised:2023-08-16 Online:2024-02-26 Published:2024-01-10
Supported by:
National Natural Science Foundation of China(12361038);National Natural Science Foundation of China(117610468);Natural Science Foundation of Gansu Province(20JR5RA411)

摘要/Abstract

摘要：

该文研究了一类具有非局部效应和非线性发生率的时滞 SEIR 系统的周期行波解. 首先, 定义基本再生数 $\Re_{0}$ 并构造适当的上下解, 将周期行波解的存在性转化为闭凸集上非单调算子的不动点问题, 利用 Schauder 不动点定理结合极限理论建立该系统周期行波解的存在性. 其次, 利用反证法结合比较原理, 建立当基本再生数 $\Re_{0} <1$ 时该系统周期行波解的不存在性.

关键词: 周期行波解, 不动点定理, 存在性

Abstract:

In this paper, the periodic traveling wave solutions to a class of delayed SEIR systems with nonlocal effects and nonlinear incidence are investigated. Firstly, the existence of periodic traveling waves is transformed into the fixed point problem of an non-monotone operator defined on a closed convex set by defining the basic reproducing number $\Re_{0}$ and constructing appropriate upper and lower solutions, and thus the existence of periodic traveling waves of the system is established by using Schauder fixed point theorem and limit theory. Secondly, the non-existence of periodic traveling wave solutions of the system is proved when the basic regeneration number $\Re_{0}<1$ by contradictory arguments and comparison principle.

Key words: Periodic traveling wave solutions, Fixed point theorem, Existence

中图分类号:

O175.14

张广新, 杨赟瑞, 宋雪. 具有非局部效应的时滞SEIR系统的周期行波解[J]. 数学物理学报, 2024, 44(1): 140-159.

Zhang Guangxin, Yang Yunrui, Song Xue. Periodic Traveling Wave Solutions of Delayed SEIR Systems with Nonlocal Effects[J]. Acta mathematica scientia,Series A, 2024, 44(1): 140-159.

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