一类同时受Markov切换和白噪声干扰的随机SIRS传染病模型  

A Class of Stochastic SIRS Infectious Disease Models Subject to Both Markov Switching and White Noise Interference

作　　者：何雪晴 韦煜明 HE Xue-qing;WEI Yu-ming(School of Mathematics and Statistics,Guangxi Normal University,Guilin 541000,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541000

出　　处：《南宁师范大学学报（自然科学版）》2021年第4期15-24,共10页Journal of Nanning Normal University：Natural Science Edition

基　　金：国家自然科学基金项目(11961074);广西科技基地和人才专项(2018AD19211)。

摘　　要：研究了一类随机SIRS传染病模型,它同时受Markov切换和白噪声干扰.首先,主要根据Ito公式、局部鞅的强大数定律以及Birkhoff遍历性定理讨论了疾病灭绝的充分条件,然后分析出该模型的解存在一个遍历平稳分布,最后用数值模拟验证了理论结果.A class of stochastic SIRS infectious disease models subject to both Markov switching and white noise interference is studied.First,the sufficient conditions for disease extinction are discussed based mainly on the Ito formula,the strong number law of local martingale,and Birkhoff’s ergodicity theorem,then the existence of a ergodic stationary distribution of solutions to the model is analyzed,and finally the theoretical results are verified with numerical simulations.

关 键 词：Markov切换 灭绝 平稳分布 ITO公式 

分 类 号：O175[理学—数学]