Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems

被引：25
|
作者：
Qi, Haokun [1 ]
Zhang, Shengqiang [1 ]
Meng, Xinzhu [1 ,2 ]
Dong, Huanhe [1 ]
机构：
[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
[2] Shandong Univ Sci & Technol, Shandong Prov & Minist Sci & Technol, State Key Lab Min Disaster Prevent & Control, Qingdao 266590, Peoples R China
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2018年 / 508卷
基金：
中国国家自然科学基金;
关键词：
Stochastic SIQS epidemic model; Periodic solution; Stationary distribution; Extinction; Markov switching; DYNAMICS ANALYSIS; POPULATION-SIZE; CHEMOSTAT MODEL; VACCINATION; BEHAVIOR; FLUCTUATION; ENVIRONMENT; EXTINCTION; DISEASES;
D O I：
10.1016/j.physa.2018.05.075
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
This paper proposes two stochastic SIQS epidemic models with periodic parameters and Markov switching. We first prove that the stochastic non-autonomous periodic system has a nontrivial positive periodic solution by using the Khasminskii's theory. Then the sufficient conditions for extinction of the disease are obtained. Furthermore, we construct suitable stochastic Lyapunov functions with regime switching to prove the existence of ergodic stationary distribution of the stochastic SIQS epidemic model. At last, some rigorous numerical simulations are presented to illustrate our theoretical results. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：223 / 241
页数：19
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