| 同时具有logistic出生和Markov切换的随机SIRS传染病模型的动力学 |
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| 引用本文： | 何雪晴,韦煜明.同时具有logistic出生和Markov切换的随机SIRS传染病模型的动力学[J].应用数学和力学,2021,42(12):1327-1337. |
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| 作者姓名： | 何雪晴 韦煜明 |
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| 作者单位： | 广西师范大学 数学与统计学院， 广西 桂林541000 |
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| 基金项目： | 国家自然科学基金（11961074）；广西科技基地和人才专项（2018AD19211） |
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| 摘 要： | 研究了一类同时具有logistic出生和Markov切换的随机SIRS传染病模型.首先通过构造合适的V函数，利用It?公式分析了随机传染病模型全局正解的存在唯一性，继而讨论出了该模型的解存在一个遍历平稳分布的结果，以及疾病灭绝的充分条件，最后给出了数值例子来说明本文得出的结论.
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| 关 键 词： | logistic出生 Markov切换 灭绝 遍历平稳分布 It?公式 |
| 收稿时间： | 2021-05-19 |
Dynamics of a Class of Stochastic SIRS Infectious Disease Models With Both Logistic Birth and Markov Switching |
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| Institution: | School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 514000, P.R.China |
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| Abstract: | A class of stochastic SIRS infectious disease models with both logistic birth and Markov switching were investigated. The uniqueness of the existence of a globally positive solution to the stochastic infectious disease model was first analyzed through construction of suitable V functions and then by means of It?’s formula. Afterwards, the results of the existence of an ergodic smooth distribution for the solution of the model and the sufficient conditions for the extinction of the disease were discussed. Finally, numerical examples were given to illustrate the conclusions. |
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