## 留言板

 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.
HE Xueqing. Dynamics of a Class of Stochastic SIRS Infectious Disease Models With Both Logistic Birth and Markov Switching[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1327-1337. doi: 10.21656/1000-0887.420140
 Citation: HE Xueqing. Dynamics of a Class of Stochastic SIRS Infectious Disease Models With Both Logistic Birth and Markov Switching[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1327-1337.

• 中图分类号: O175

## Dynamics of a Class of Stochastic SIRS Infectious Disease Models With Both Logistic Birth and Markov Switching

Funds:

The National Natural Science Foundation of China(11961074)

• 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Itô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.
•  KERMACK W O, MCKENDRICK A G. A contribution to the mathematical theory of epidemics[J].Proceedings of the Royal Society of London,1927,115(772): 700-721. [2]MA Zhien, ZHOU Yicang, WU Jianhong.Modeling and Dynamics of Infectious Diseases[M]. New Jersey: World Scientific Publishing Company, 2009. [3]LIU W M, LEVIN S A, IWASA Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models[J].Journal of Mathematical Biology,1986,23(2): 187-204. [4]CAI Y, KANG Y, BANERJEE M, et al. A stochastic SIRS epidemic model with infectious force under intervention strategies[J].Differential Equations,2015,259(12): 7463-7502. [5]ZHANG Juan, LI Jianquan, MA Zhien. Global analysis of SIR epidemic models with population size dependent contact rate[J].Journal of Engineering Mathematics,2004,21(2): 259-267. [6]MCKENDRICK A G. Applications of mathematics to medical problems[J].Proceedings of the Edinburgh Mathematical Society,1925,44: 98-130. [7]KEELING M J, ROHANI P.Modeling Infectious Diseases in Human and Animals[M]. New Jersey: Princeton University Press, 2008. [8]OKSENDAL B.Stochastic Differential Equations: an Introduction With Applications[M]. New York: Springer, 1980. [9]LUO Q, MAO X. Stochastic population dynamics under regime switching[J].Journal of Mathematical Analysis and Applications,2007,334(1): 69-84. [10]KHASMINSKII R Z, ZHU C, YIN G. Stability of regime-switching diffusions[J].Stochastic Processes and Their Applications,2007,117(8): 1037-1051. [11]MAO X.Stochastic Differential Equations and Applications[M]. Sawston: Horwood Publishing, 1997. [12]HIGHAM D J. An algorithmic introduction to numerical simulation of stochastic differential equations[J].SIAM Review,2001,43(3): 525-546.

##### 计量
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##### 出版历程
• 收稿日期:  2021-05-19
• 修回日期:  2021-06-23
• 网络出版日期:  2021-12-31

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