A stochastic switched SIRS epidemic model with nonlinear incidence and vaccination:Stationary distribution and extinction  

作　　者：Xin Zhao Xin He Tao Feng Zhipeng Qiu 

机构地区：[1]Department of Mathematics Nanjing University of Science and Technology Nanjing 210094,P.R.China

出　　处：《International Journal of Biomathematics》2020年第3期137-164,共28页生物数学学报（英文版）

基　　金：Z.Qiu is supported by the National Natural Science Foundation of China(NSFC)grant No.11671206;X.Zhao is supported by the Scholarship Foundation of China Scholarship Council grant No.201906840072;T.Feng is supported by the Scholarship Foundation of China Scholarship Council grant No.201806840120;the Out-standing Chinese and Foreign Youth Exchange Program of China Association of Science and Technology;the Fundamental Research Funds for the Central Universities grant No.30918011339.

摘　　要：In this paper,a stochastic epidemic system with both switching noise and white noise is proposed to research the dynamics of the diseases.Nonlinear incidence and vaccination strategies are also considered in the proposed model.By using the method of stochastic analysis,we point out the key parameters that determine the persistence and extinction of the diseases.Specifically,if R0^s is greater than 0,the stochastic system has a unique ergodic stationary distribution;while if R ^* is less than 0,the diseases will be extinct at an exponential rate.

关 键 词：Stochastic SIRS epidemic model nonlinear incidence markov switch sta-tionary distribution EXTINCTION 

分 类 号：O17[理学—数学]