一类非局部扩散的分布时滞SVIR 模型的行波解

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2349-2370.

一类非局部扩散的分布时滞SVIR 模型的行波解

邱小勤(), 杨赟瑞^*()

兰州交通大学数理学院兰州 730070

收稿日期:2025-08-28 修回日期:2025-12-05 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 杨赟瑞 E-mail:xq050621@163.com;lily1979101@163.com
作者简介:邱小勤, E-mail: xq050621@163.com
基金资助:
国家自然科学基金(12361038);甘肃省基础研究创新群体项目(25JRRA805)

Traveling Wave Solutions to a Class of SVIR Model with Distributed Delay and Nonlocal Dispersal

Xiaoqin Qiu(), Yunrui Yang^*()

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

Received:2025-08-28 Revised:2025-12-05 Online:2026-12-26 Published:2026-08-14
Contact: Yunrui Yang E-mail:xq050621@163.com;lily1979101@163.com
Supported by:
National Natural Science Foundation of China(12361038);Foundation for Innovative Fundamental Research Group Project of Gansu Province(25JRRA805)

摘要/Abstract

摘要：

研究了一类非局部扩散的分布时滞SVIR 模型的行波解. 通过上、下解的构造和Schauder 不动点定理、极限理论与 Lyapunov 函数方法建立了该模型行波解的存在性. 特别地, 在验证行波解满足的渐近边界条件时, 由于分布时滞的出现, 使行波解有界性的建立和Lyapunov 函数的构造变得困难, 需要更为细致的分析技术. 此外, 基于渐近传播理论和反证法得到了该模型行波解的不存在性. 这不仅将无时滞和离散时滞SVIR 模型行波解的研究结果推广到了分布时滞情形, 还完善了考虑疫苗接种策略的传染病模型行波解的研究.

关键词: 非局部扩散, 分布时滞, 行波解, 存在性, 不存在性

Abstract:

Traveling wave solutions for a class of SVIR model with distributed delay and nonlocal dispersal are considered. By the construction of upper and lower solutions and with the help of Schauder's fixed-point theorem, limit theory, analytical techniques, and Lyapunov function methods, the existence of traveling wave solutions for this model is established. Particularly, it is essential to use analytical techniques more detailed for testifying the asymptotic boundary conditions of traveling waves since it becomes more difficult for the boundedness of traveling waves and the construction of Lyapunov functions for the presence of distributed delay in the model. Moreover, the non-existence of traveling waves is obtained by asymptotic spreading theory and a contradiction argument. Therefore, the results on traveling waves for delay-free and discrete time-delay SVIR models are not only extended to the case of distributed delay, but the research of traveling waves in vaccination-stratified epidemic models is enriched and completed.

Key words: nonlocal dispersal, distributed delay, traveling wave solutions, existence, nonexistence

中图分类号:

O175

邱小勤, 杨赟瑞. 一类非局部扩散的分布时滞SVIR 模型的行波解[J]. 数学物理学报, 2026, 46(6): 2349-2370.

Xiaoqin Qiu, Yunrui Yang. Traveling Wave Solutions to a Class of SVIR Model with Distributed Delay and Nonlocal Dispersal[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2349-2370.

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