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

被引：0
|
作者：
ZHANG Weiwei [1 ,2 ]
MENG Xinzhu [1 ,2 ,3 ]
DONG Yulin [2 ]
机构：
[1] College of Electrical Engineering and Automation, Shandong University of Science and Technology
[2] College of Mathematics and Systems Science, Shandong University of Science and Technology
[3] Key Laboratory of Mining Disaster Prevention and Control Cofounded by Shan-dong Province and the Ministry of Science and Technology, Shandong University of Science and Technology
来源：
Journal of Systems Science & Complexity | 2019年 / 32卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Extinction and stochastic permanence; Markov chain; periodic solution; stationary distribution and ergodicity; stochastic SIRI epidemic model;
D O I：
暂无
中图分类号：
O175 [微分方程、积分方程];
学科分类号：
070104 ;
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.
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页码：1104 / 1124
页数：21
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