具有随机效应的SIRI传染病模型的定性分析  

The Qualitative Analysis of SIRI Epidemic Model with Stochastic Effects

作　　者：雷桥[1] 杨志春[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2016年第1期81-85,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11471061);重庆市自然科学基金(No.CQCSTC2014JCYJA40004);重庆市高校创新团队计划(No.KJTD201308);重庆师范大学研究生科研创新项目(No.YKC15015)

摘　　要：研究了具双线性传染率的随机SIRI传染病模型的动态行为。首先,利用随机微分方程理论构造V函数,结合伊藤公式等方法,给出了随机SIRI传染病模型解的存在唯一性。然后,给出了随机模型平衡点稳定性和振荡性质,即当基本再生数小于等于1时,随机模型的无病平衡点是全局随机渐近稳定的,当基本再生数大于1时,随机模型的解围绕确定性模型的地方病平衡点是随机振荡。In this paper, we considered dynamical behaviors of Stochastic SIRI epidemic model with bi-linear incidence rate. Firstly, we show that the stochastic SIRI epidemic model has a unique global positive solution by using lto formula, that is to say the solution of the model will not explode to infinite in a finite time. In addition, the stability and oscillation is investigated for the equilibria. That is, the disease-free equilibrium of the stochastic model is globally asymptotically stable in stochastic meaning when the basic reproduction number is equal or lesser than one, and the solution is fluctuate around the endemic equilibrium of the deterministic model when the basic reproduction number is greater than one.

关 键 词：随机传染病模型 SIRI 全局渐近稳定 振荡 

分 类 号：O175[理学—数学]