A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate

被引：32
|
作者：
Liu, Qun [1 ]
Jiang, Daqing [2 ,3 ,4 ]
Hayat, Tasawar [4 ,5 ]
Alsaedi, Ahmed [4 ]
Ahmad, Bashir [4 ]
机构：
[1] Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat MOE, Changchun 130024, Jilin, Peoples R China
[2] China Univ Petr East China, Key Lab Unconvent Oil & Gas Dev, Minist Educ, Qingdao 266580, Peoples R China
[3] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China
[4] King Abdulaziz Univ, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah, Saudi Arabia
[5] Quaid I Azam Univ, Dept Math, Islamabad 45320, Pakistan
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2020年 / 551卷
基金：
中国国家自然科学基金;
关键词：
SIRS epidemic model; Logistic growth; General nonlinear incidence rate; Stationary distribution; Ergodicity; STATIONARY DISTRIBUTION; NUMERICAL SIMULATIONS; MEDIA; INTERFERENCE; PERSISTENCE;
D O I：
10.1016/j.physa.2020.124152
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we consider a stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic Lyapunov function, which provides us a good description of persistence. We find that the hypothetical conditions on the nonlinear function are relative weak and valid for many forms of incidence rate. (C) 2020 Elsevier B.V. All rights reserved.
引用
收藏
页数：11
相关论文
共 50 条
  • [1] A stochastic SIRS epidemic model with nonlinear incidence rate
    Cai, Yongli
    Kang, Yun
    Wang, Weiming
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2017, 305 : 221 - 240
  • [2] Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence
    Rajasekar, S. P.
    Pitchaimani, M.
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2020, 377
  • [3] Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence
    Wang, Huyi
    Zhang, Ge
    Chen, Tao
    Li, Zhiming
    [J]. MATHEMATICS, 2023, 11 (07)
  • [4] THRESHOLD DYNAMICS IN A STOCHASTIC SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE
    Zhao, Yanan
    Zhang, Xiaoying
    O'Regan, Donal
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2019, 9 (06): : 2096 - 2110
  • [5] The Threshold of a Stochastic SIRS Epidemic Model with a General Incidence
    Lakhal, Mohammed
    El Guendouz, Tarik
    Taki, Regragui
    El Fatini, Mohamed
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2024, 47 (04)
  • [6] BIFURCATIONS OF AN SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE
    Hu, Zhixing
    Bi, Ping
    Ma, Wanbiao
    Ruan, Shigui
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2011, 15 (01): : 93 - 112
  • [7] Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model with saturated incidence rate
    N'zi, Modeste
    Kanga, Gerard
    [J]. RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2016, 24 (01) : 65 - 77
  • [8] Bifurcations of an SIRS epidemic model with a general saturated incidence rate
    Zhang, Fang
    Cui, Wenzhe
    Dai, Yanfei
    Zhao, Yulin
    [J]. MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2022, 19 (11) : 10710 - 10730
  • [9] On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate
    Buonomo, Bruno
    Rionero, Salvatore
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (08) : 4010 - 4016
  • [10] Stability of a delayed SIRS epidemic model with a nonlinear incidence rate
    Xu, Rui
    Ma, Zhien
    [J]. CHAOS SOLITONS & FRACTALS, 2009, 41 (05) : 2319 - 2325
12345