Periodic Solution and Ergodic Stationary Distribution of Stochastic SIRI Epidemic Systems with Nonlinear Perturbations  

作　　者：ZHANG Weiwei MENG Xinzhu DONG Yulin 

机构地区：[1]College of Electrical Engineering and Automation,Shandong University of Science and Technology,Qingdao 266590,China [2]College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,China [3]State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology,Shandong University of Science and Technology,Qingdao 266590,China

出　　处：《Journal of Systems Science & Complexity》2019年第4期1104-1124,共21页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.11371230;the Research Fund for the Taishan Scholar Project of Shandong Province of China;the SDUST Research Fund under Grant No.2014TDJH102

摘　　要：This paper formulates two stochastic nonautonomous SIRI epidemic systems with nonlinear perturbations.The main aim of this study is to investigate stochastic dynamics of the two SIRI epidemic systems and obtain their thresholds.For the nonautonomous stochastic SIRI epidemic system with white noise,the authors provide analytic results regarding the stochastic boundedness,stochastic permanence and persistence in mean.Moreover,the authors prove that the system has at least one nontrivial positive T-periodic solution by using Lyapunov function and Hasminskii’s theory.For the system with Markov conversion,the authors establish sufficient conditions for positive recurrence and existence of ergodic stationary distribution.In addition,sufficient conditions for the extinction of disease are obtained.Finally,numerical simulations are introduced to illustrate the main results.This paper formulates two stochastic nonautonomous SIRI epidemic systems with nonlinear perturbations. The main aim of this study is to investigate stochastic dynamics of the two SIRI epidemic systems and obtain their thresholds. For the nonautonomous stochastic SIRI epidemic system with white noise, the authors provide analytic results regarding the stochastic boundedness, stochastic permanence and persistence in mean. Moreover, the authors prove that the system has at least one nontrivial positive T-periodic solution by using Lyapunov function and Hasminskii’s theory. For the system with Markov conversion, the authors establish sufficient conditions for positive recurrence and existence of ergodic stationary distribution. In addition, sufficient conditions for the extinction of disease are obtained. Finally, numerical simulations are introduced to illustrate the main results.

关 键 词：Extinction and STOCHASTIC PERMANENCE Markov chain periodic solution stationary distribution and ERGODICITY STOCHASTIC SIRI EPIDEMIC model 

分 类 号：O1[理学—数学]