The stationary distribution in a class of stochastic SIRS epidemic models with non-monotonic incidence and degenerate diffusion

被引：7
|
作者：
Tuerxun, Nafeisha [1 ]
Wen, Buyu [1 ]
Teng, Zhidong [1 ]
机构：
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
来源：
MATHEMATICS AND COMPUTERS IN SIMULATION | 2021年 / 182卷
基金：
中国国家自然科学基金;
关键词：
Stochastic SIRS epidemic model; Degenerate diffusion; Non-monotonic incidence; Basic reproduction number; Markov semigroup; Stationary distribution; ASYMPTOTIC PROPERTIES; NUMERICAL-SIMULATION; BEHAVIOR; PERTURBATION; EXTINCTION; STABILITY; DELAY;
D O I：
10.1016/j.matcom.2020.03.008
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
A class of stochastic SIRS epidemic models with non-monotonic incidence and degenerate diffusion is investigated. By using the Lyapunov function method, the existence of global positive solutions and the ultimate boundedness with probability one are obtained. By using the Markov semigroups theory, Fokker-Planck equation and Khasminskii functions, the existence of unique stationary distribution for the model is established. That is, when the stochastic basic reproduction number R-0(S) > 1 and some extra conditions are satisfied then the distribution density of any positive solutions of the model converges to a unique invariant density as t -> +infinity. Finally, the main conclusions and open problems are illustrated and verified by the numerical simulations. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：888 / 912
页数：25
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