Extinction and Stationary Distribution of a Stochastic SIR Epidemic Model with Jumps  

作　　者：ZHU Min LI Jun-ping ZHU Yong-xiang 朱敏;李俊平;朱永祥(School of Mathematics and Statistics,Central South University;College of Electrical and Information Engineering,Hunan University of Technology;College of Traffic Engineering,Hunan University of Technology)

机构地区：[1]School of Mathematics and Statistics, Central South University, Changsha 410085, China [2]College of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China [3]College of Traffic Engineering, Hunan University of Technology, Zhuzhou 412007, China

出　　处：《Journal of Donghua University(English Edition)》2016年第6期843-850,共8页东华大学学报（英文版）

基　　金：Natural Science Foundation of Hunan University of Technology,China(No.2012HZX08);the Special Foundation of National Independent Innovation Demonstration Area Construction of Zhuzhou(Applied Basic Research),China

摘　　要：A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.A stochastic susceptible-infective-recovered （ SIR ） epidemic model with jumps was considered. The contributions of this paper are as follows. （ 1 ） The stochastic differential equation （SDE） associated with the model has a unique global positive solution; （2） the results reveal that the solution of this epidemic model will be stochastically ultimately bounded, and the non-linear SDE admits a unique stationary distribution under certain parametric conditions; （3） the coefficients play an important role in the extinction of the diseases.

关 键 词：susceptible-infective-recovered （SIR） epidemic model stochastically ultimately bounded FELLER stationary distribution EXTINCTION lumps 

分 类 号：O211.63[理学—概率论与数理统计]