具有信息干预和饱和发生率的随机SIRS传染病模型的灭绝性与持久性  

Permanence and Extinction of a Stochastic SIRS Epidemic Model with Information Intervention and Saturated Rate

作　　者：秦闯亮 杜金姬 俞迎达 QIN Chuang-liang;DU Jin-ji;YU Ying-da(School of Mathematics and Statistics,Xinyang College,Xinyang 464000,China)

机构地区：[1]信阳学院数学与统计学院,河南信阳464000

出　　处：《数学的实践与认识》2021年第10期274-280,共7页Mathematics in Practice and Theory

基　　金：河南省高等学校重点科研项目(20B110017);信阳市规划项目(2019TS010);信阳学院资助项目(2018LYB02,2018LYB09)。

摘　　要：讨论了一类具有信息干预和饱和发生的双随机SIRS传染病模型的动力学行为.通过构造C2函数,证明了双随机模型全局正解的存在唯一性.通过借助随机分析理论,获得了疾病的灭绝性和持久性的充分条件.最后,通过数值模拟验证了该研究的结论,并进一步研究了信息干预对疾病的影响.In this paper,we discuss the dynamics of a two-stochastic SIRS epidemic model with information intervention and saturation.By constructing C2 functions,we prove the existence and uniqueness of the globally positive solution of the two-stochastic SIRS epidemic model.By using stochastic analysis theory,we obtain the extinction and the sufficient conditions to guarantee the permanence of epidemic.Finally,the conclusions of this study are validated by numerical simulation,and the effect of information intervention on disease is further studied.

关 键 词：随机SIRS模型 信息干预 灭绝性 持久性 

分 类 号：O211.6[理学—概率论与数理统计] R181[理学—数学]