标题：Periodic Solution and Ergodic Stationary Distribution of Stochastic SIRI Epidemic Systems with Nonlinear Perturbations
作者：Zhang Weiwei; Meng Xinzhu; Dong Yulin
作者机构：[Zhang Weiwei; Meng Xinzhu] Shandong Univ Sci & Technol, Coll Elect Engn & Automat, Qingdao 266590, Shandong, Peoples R China.; [Zhang Weiwei; Meng 更多
通讯作者：Meng, XZ;Meng, XZ;Meng, XZ;Meng, Xinzhu
通讯作者地址：[Meng, XZ]Shandong Univ Sci & Technol, Coll Elect Engn & Automat, Qingdao 266590, Shandong, Peoples R China;[Meng, XZ]Shandong Univ Sci & Technol, Col 更多
来源：JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
关键词：Extinction and stochastic permanence; Markov chain; periodic solution;; stationary distribution and ergodicity; stochastic SIRI epidemic model
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.