Markov切换下含疫苗接种和垂直感染的随机SIRS模型性质  

The Properties of Stochastic SIRS Model with Vaccination andVertical Transmission Under Markovian Switching

作　　者：董朝丽[1] 陆万春[2] DONG Zhaoli;LU Wanchun(Nanchang Business College,Jiangxi Agricultural University,Ganjiang New District Jiangxi 332020,China;Department of Mathematics,Pingxiang University,Pingxiang Jiangxi 337000,China)

机构地区：[1]江西农业大学南昌商学院,江西赣江新区332020 [2]萍乡学院数学系,江西萍乡337000

出　　处：《江西师范大学学报（自然科学版）》2023年第4期336-341,共6页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(62063029);江西省教育厅科学技术研究课题(GJJ209103)资助项目.

摘　　要：该文研究了一类含Markov机制切换和疫苗接种及垂直感染的随机SIRS模型的动力学性质,通过构造带切换的Lyapunov函数,研究了模型具有平稳分布的判别条件,并研究了在模型中疾病趋于灭绝的阈值.最后通过举例来验证研究结果.结果表明:模型具有平稳分布和趋于灭绝的阈值是相同的.The dynamic properties of a class of stochastic SIRS model with vaccination and vertical transmission under Markovian switching are studied.By constructing the Lyapunov function with switching,the discriminant conditions of the model with stationary distribution are studied,and the threshold of disease tending to extinction in the model is studied.Finally,example is presented to verify the theoretical results.The conclusions show that the threshold of the model for stationary distribution and extinction is consistent.

关 键 词：Markov机制切换 随机SIRS模型 疫苗接种 垂直感染 动力性质 

分 类 号：O211.6[理学—概率论与数理统计] O29[理学—数学]