转换机制下具有非线性扰动的随机SIVS传染病模型的定性分析

数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 1218-1234.

转换机制下具有非线性扰动的随机SIVS传染病模型的定性分析

张仲华*(),张倩()

^{西安科技大学理学院西安 710054}

收稿日期:2020-09-11 出版日期:2021-08-26 发布日期:2021-08-09
通讯作者: 张仲华 E-mail:wwwzhangzhonghua@163.com;994926272@qq.com
作者简介:张倩, E-mail: 994926272@qq.com
基金资助:
国家自然科学基金(11201277)

Qualitative Analysis of a Stochastic SIVS Epidemic Model with Nonlinear Perturbations Under Regime Switching

Zhonghua Zhang*(),Qian Zhang()

^{School of Sciences, Xi'an University of Science and Technology, Xi'an 710054}

Received:2020-09-11 Online:2021-08-26 Published:2021-08-09
Contact: Zhonghua Zhang E-mail:wwwzhangzhonghua@163.com;994926272@qq.com
Supported by:
the NSFC(11201277)

摘要/Abstract

摘要：

该文考虑随机环境因素的影响，建立了一类转换机制下具有非线性扰动的SIVS模型.对于具有白噪声的非自治随机SIVS流行病系统，给出了解的随机有界性和随机持久性的结果，并利用李雅普诺夫函数和Has'minskii周期解理论证明了非平凡正周期解的存在性.对于具有马尔科夫变换的系统，建立了遍历平稳分布的充分条件，分别得到了染病者在平均意义下持久性的阈值和灭绝性的阈值.最后，通过数值模拟支撑了理论结果.

关键词: 随机SIVS传染病模型, 非线性扰动, 马尔科夫链, 非线性发病率

Abstract:

In this paper, we present a stochastic SIVS epidemic model with nonlinear perturbations under regime switching. For the non-autonomous stochastic SIVS epidemic system with white noise, we provide results regarding the stochastic boundedness, stochastic permanence in mean, and we prove that the system has at least one nontrivial positive T-periodic solution by using Lyapunov function and Hasminskii's theory. For the system with Markov conversion, we establish sufficient conditions for existence of ergodic stationary distribution, and the thresholds for persistence in mean and the extinction of infected persons was obtained, respectively. Finally, some numerical simulations are carried out to support the theoretical results.

Key words: Stochastic SIVS epidemic model, Nonlinear perturbation, Markov chain, Nonlinear incidence

中图分类号:

O211.63

张仲华,张倩. 转换机制下具有非线性扰动的随机SIVS传染病模型的定性分析[J]. 数学物理学报, 2021, 41(4): 1218-1234.

Zhonghua Zhang,Qian Zhang. Qualitative Analysis of a Stochastic SIVS Epidemic Model with Nonlinear Perturbations Under Regime Switching[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1218-1234.

图/表 3

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