Two-group SIR Epidemic Model with Stochastic Perturbation  

作　　者：Chun Yan JI Da Qing JIANG Ning Zhong SHI 

机构地区：[1]School of Mathematics and Statistics,Changshu Institute of Technology [2]School of Mathematics and Statistics,Northeast Normal University

出　　处：《Acta Mathematica Sinica,English Series》2012年第12期2545-2560,共16页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10971021);the Ministry of Education of China (Grant No. 109051);the Ph.D. Programs Foundation of Ministry of China (Grant No. 200918);the Graduate Innovative Research Project of NENU (Grant No. 09SSXT117)

摘　　要：A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.

关 键 词：Stochastic two-group SIR model disease-free equilibrium endemic equilibrium stochastic Lyapunov function asymptotically stable in the large 

分 类 号：O211.6[理学—概率论与数理统计]