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

页码：888 / 912

页数：25

共 50 条

[1] An SIRS epidemic model with pulse vaccination and non-monotonic incidence rate
Zhang, Xiao-Bing
Huo, Hai-Feng
Xiang, Hong
Meng, Xin-You
[J]. NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2013, 8 : 13 - 21
[2] Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate
Gakkhar, Sunita
Negi, Kuldeep
[J]. CHAOS SOLITONS & FRACTALS, 2008, 35 (03) : 626 - 638
[3] Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion
Lan, Guijie
Chen, Zhewen
Wei, Chunjin
Zhang, Shuwen
[J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 511 : 61 - 77
[4] Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate
Muroya, Yoshiaki
Enatsu, Yoichi
Nakata, Yukihiko
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 377 (01) : 1 - 14
[5] STATIONARY DISTRIBUTION OF STOCHASTIC SIRS EPIDEMIC MODEL WITH STANDARD INCIDENCE
Zhao, Yanan
Lin, Yuguo
Jiang, Daqing
Mao, Xuerong
Li, Yong
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2016, 21 (07): : 2363 - 2378
[6] Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence
Lahrouz, Aadil
Omani, Lahcen
[J]. STATISTICS & PROBABILITY LETTERS, 2013, 83 (04) : 960 - 968
[7] Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence
Liu, Qun
Jiang, Daqing
Shi, Ningzhong
Hayat, Tasawar
Alsaedi, Ahmed
[J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2017, 469 : 510 - 517
[8] Threshold Behavior in a Class of Stochastic SIRS Epidemic Models With Nonlinear Incidence
Tang, Tingting
Teng, Zhidong
Li, Zhiming
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2015, 33 (06) : 994 - 1019
[9] Dynamics and stationary distribution of a stochastic SIRS epidemic model with a general incidence and immunity
Tao Chen
Zhiming Li
[J]. Boundary Value Problems, 2022
[10] Dynamics and stationary distribution of a stochastic SIRS epidemic model with a general incidence and immunity
Chen, Tao
Li, Zhiming
[J]. BOUNDARY VALUE PROBLEMS, 2022, 2022 (01)

← 1 2 3 4 5 →