具有媒体报道的 SVIR 传染病模型的生存性分析

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1595-1606.

具有媒体报道的 SVIR 传染病模型的生存性分析

李丹¹,魏凤英^2,^*(),毛学荣³

¹福州大学数学与统计学院福州 350116
²福州大学运筹学与控制论福建省高校重点实验室福州 350116
³思克莱德大学数学与统计系格拉斯哥 G1 1XH

收稿日期:2022-04-22 修回日期:2022-10-31 出版日期:2023-10-26 发布日期:2023-08-09
通讯作者: 魏凤英 E-mail:weifengying@fzu.edu.cn
基金资助:
国家自然科学基金-国际(地区)合作与交流项目(61911530398);福建省科技厅项目(2021L3018);福建省自然科学基金(2021J01621);英国皇家学会(WM160014);英国皇家学会(英国皇家学会沃尔夫森研究优异奖);英国皇家学会和牛顿基金(NA160317);英国皇家学会和牛顿基金(皇家学会-牛顿高级奖学金);工程和物理科学研究委员会(EP/K503174/1)

Survival Analysis of an SVIR Epidemic Model with Media Coverage

Li Dan¹,Wei Fengying^2,^*(),Mao Xuerong³

¹School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116
²Key Laboratory of Operations Research and Control of Universities in Fujian, Fuzhou University, Fuzhou 350116
³Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK

Received:2022-04-22 Revised:2022-10-31 Online:2023-10-26 Published:2023-08-09
Contact: Fengying Wei E-mail:weifengying@fzu.edu.cn
Supported by:
National Natural Science Foundation of China(61911530398);Special Projects of the Central Government Guiding Local Science, Technology Development(2021L3018);Natural Science Foundation of Fujian Province of China(2021J01621);Royal Society, UK(WM160014);Royal Society, UK (Royal Society Wolfson Research Merit Award);Royal Society and the Newton Fund, UK(NA160317);Royal Society and the Newton Fund, UK (Royal Society-Newton Advanced Fellowship);EPSRC, the Engineering and Physical Sciences Research Council(EP/K503174/1)

摘要/Abstract

摘要：

该文研究了具有Logistic增长和媒体报道的饱和发生率的随机SVIR模型. 为了研究模型的动力学性质, 首先证明了随机模型全局正解的存在唯一性, 其次通过构造合适的李雅普诺夫函数, 探究疾病持久和灭绝的充分性条件. 研究表明: 当${R}_{0}^{s}>1$时, 疾病长时间持续存在. 当${R}_{0}^{e}<1$时, 疾病在流行一段时间后灭绝. 最后, 通过数值模拟验证了以上结论.

关键词: 传染病模型, 疫苗, 媒体报道, 持久性与灭绝性, 平稳分布

Abstract:

We consider the long-term properties of a stochastic SVIR epidemic model with media coverage and the logistic growth in this paper. We firstly derive the fitness of a unique global positive solution. Then we construct appropriate Lyapunov functions and obtain the existence of ergodic stationary distribution when ${R}_{0}^{s}>1$ is valid, and also derive sufficient conditions for persistence in the mean. Moreover, the exponential extinction to the density of the infected is figured out when ${R}_{0}^{e}<1$ holds.

Key words: Epidemic model, Vaccination, Media coverage, Persistence and extinction, Stationary distribution

中图分类号:

O175.13

李丹,魏凤英,毛学荣. 具有媒体报道的 SVIR 传染病模型的生存性分析[J]. 数学物理学报, 2023, 43(5): 1595-1606.

Li Dan,Wei Fengying,Mao Xuerong. Survival Analysis of an SVIR Epidemic Model with Media Coverage[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1595-1606.

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