一类受媒体报道影响的随机SIRI传染病模型的定性分析  

Qualitative Analysis of a Kind of Stochastic SIRI Epidemic Model with Media Coverage

作　　者：刘变红 刘桂荣[2] LIU Bian-hong;LIU Gui-rong(Department of Mathematics,Luliang University,Lishi Shanxi 033001,China;Department of Mathematics,Shanxi University,Shanxi Taiyuan 030006,China)

机构地区：[1]吕梁学院数学系,山西离石033001 [2]山西大学数学科学学院,山西太原030006

出　　处：《吕梁学院学报》2020年第2期14-18,共5页Journal of Lyuiang University

基　　金：国家自然科学基金(201801D121009).

摘　　要：考虑了一类媒介报道对SIRI传染病传播影响的随机数学模型,研究了该传染病模型的动力学性态.利用It公式和Lyapunov方法等相关理论,证明了该随机系统全局正解的存在唯一性,并得到了围绕无病平衡点的解的渐近性质,且证明了地方病平衡点的存在唯一性.推广了已有文献中的相关结论.A kind of stochastic SIRI epidemic model with media coverage is considered,and the dynamic behaviour of this model is discussed.By using It's formula and Lyapunov method and the relevant theory,the existence and uniqueness of the global positive solution of the stochastic model is proved,then the asymptotic properties of the solution around the disease-free equilibrium is obtained,and the existence and uniqueness of the endemic equilibrium is testified.These criteria have generalized the corresponding results in some existing papers.

关 键 词：随机SIRI传染病模型 It公式 LYAPUNOV方法 无病平衡点 地方病平衡点 

分 类 号：O193[理学—数学]