The asymptotic behavior and ergodicity of stochastically perturbed SVIR epidemic model  

作　　者：Yanan Zhao Daqing Jiang 

机构地区：[1]School of Mathematics and Statistics, Northeast Normal University Changchun 130024, Jilin, P. R. China [2]School of Science, Changchun University Changchun 130022, Jilin, P. R. China [3]Nonlinear Analysis and Applied Mathematics (NAAM) Research Group King Abdulaziz University, Jeddah, Saudi Arabia [4]College of Science, China University of Petroleum (East China) Qingdao 266580, P. R. China

出　　处：《International Journal of Biomathematics》2016年第3期177-190,共14页生物数学学报（英文版）

摘　　要：In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.

关 键 词：Stochastic SVIR epidemic model disease-free equilibrium stationary distri-bution ERGODICITY stochastic Lyapunov functions. 

分 类 号：O175.1[理学—数学] TP273.2[理学—基础数学]