具有时滞的离散扩散疫苗接种模型的行波解

具有时滞的离散扩散疫苗接种模型的行波解

Traveling Waves for a Discrete Diffusive Vaccination Model with Delay

摘要/Abstract

图/表 3

参考文献 17

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 858-874.

武文斌,任雪(),张冉^*()

黑龙江大学数学科学学院哈尔滨 150080; 黑龙江省复杂系统理论与计算重点实验室哈尔滨 150080

收稿日期:2024-05-17 修回日期:2025-01-03 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *张冉, Email: ranzhang@hlju.edu.cn
作者简介:任雪，Email: xueren@hlju.edu.cn
基金资助:
国家自然科学基金(12101309);国家自然科学基金(12371490);国家自然科学基金(12401638);黑龙江省自然科学基金(YQ2024A011);黑龙江省自然科学基金(JQ2023A005);黑龙江省省属高等学校基本科研业务费(2022-KYYWF-1113);黑龙江省省属高等学校基本科研业务费(2023-KYYWF-1493);黑龙江大学杰出青年科学基金(JCL202203)

Wu Wenbin,Ren Xue(),Zhang Ran^*()

School of Mathematical Sciences, Heilongjiang University, Harbin 150080; Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Harbin 150080

Received:2024-05-17 Revised:2025-01-03 Online:2025-06-26 Published:2025-06-20
Supported by:
NSFC(12101309);NSFC(12371490);NSFC(12401638);Natural Science Foundation of Helongjiang Province(YQ2024A011);Natural Science Foundation of Helongjiang Province(JQ2023A005);Fundamental Research Funds for the Colleges and Universities in Heilongjiang Province(2022-KYYWF-1113);Fundamental Research Funds for the Colleges and Universities in Heilongjiang Province(2023-KYYWF-1493);Outstanding Youth Funds of Heilongjiang University(JCL202203)

摘要：

该文研究具有时滞的离散扩散疫苗接种模型的行波解. 该模型综合考虑了人口的自然增长、感染、治愈以及疫苗接种等因素, 并考虑了易感者、接种疫苗者与感染者之间的直接接触感染的时滞效应. 通过建立适当的格点动力系统, 得到了模型行波解的存在性和渐近行为. 进一步结果表明, 疫苗接种率、染病者的移动能力以及传播率对行波解的形成和速度有重要影响, 可能导致行波解的加速或减缓. 这些发现对于制定有效的疫苗接种策略和控制传染病的传播具有重要的理论和实际意义.

关键词: 行波解, 疫苗接种, 扩散传染病模型, 格点动力系统, Lyapunov 泛函

Abstract:

This paper considers the traveling wave solutions of a discrete diffusion vaccination model with time delay. The model comprehensively considers factors such as natural population growth, infection, recovery, and vaccination, as well as the time delay effect of direct contact infection between susceptible individuals, vaccinated individuals, and infected individuals. By establishing appropriate lattice dynamical system, the existence and asymptotic behavior of the traveling wave solutions are obtained. Further results indicate that vaccination rates, the mobility of infected individuals, and transmission rates have a significant impact on the formation and speed of traveling wave solutions. These findings have important theoretical and practical significance for formulating effective vaccination strategies and controlling the spread of infectious diseases.

Key words: traveling wave solution, vaccination, diffusion epidemic model, lattice dynamical system, Lyapunov functional

中图分类号:

O175

武文斌, 任雪, 张冉. 具有时滞的离散扩散疫苗接种模型的行波解[J]. 数学物理学报, 2025, 45(3): 858-874.

Wu Wenbin, Ren Xue, Zhang Ran. Traveling Waves for a Discrete Diffusive Vaccination Model with Delay[J]. Acta mathematica scientia,Series A, 2025, 45(3): 858-874.

图1

在 $\Re_0=5.568$ , $c^*<c=2$ 时, 系统(2.3)的解曲线."

图1

图2

当 $\Re_0=0.872$ , $c^*>c=0.4$ 时, 系统(2.3)的解曲线."

图2

图3

参数 $\beta_1$ , $\beta_2$ , $d_3$ , $\delta$ 的变化对最小波速 $c^*$ 的影响."

图3

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