Stability of stochastic SIRS epidemic models with saturated incidence rates and delay

被引：17
|
作者：
Zhong, Xiaoyun [1 ,2 ]
Guo, Shangjiang [1 ]
Peng, Minfang [2 ]
机构：
[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
[2] Hunan Univ, Coll Elect & Informat Engn, Changsha, Hunan, Peoples R China
来源：
STOCHASTIC ANALYSIS AND APPLICATIONS | 2017年 / 35卷 / 01期
基金：
国家教育部博士点专项基金资助;
关键词：
Stochastic SIRS model; delay; Ito's formula; stability in probability; Euler-Maruyama method; TEMPORARY IMMUNITY; GLOBAL STABILITY; DIFFERENTIAL-EQUATIONS; NONLINEAR INCIDENCE; TIME DELAYS; PERTURBATIONS; EXTINCTION; DYNAMICS; SYSTEM;
D O I：
10.1080/07362994.2016.1244644
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we consider stochastic susceptible-infected-removed-susceptible (SIRS) epidemic models with saturated incidence rates and delay. We investigate the stochastic stability in probability of the disease-free and endemic equilibria for the stochastic dynamic model with variability in the natural death rate, and the stochastic stability in probability of the endemic equilibrium for the dynamic model when the variability in the environment is proportional to a deviation between the state of the system and the endemic equilibrium. The numerical experiments are provided to support our theoretical results.
引用
收藏
页码：1 / 26
页数：26
相关论文
共 50 条
  • [1] Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence
    Liu, Qun
    Chen, Qingmei
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2015, 428 : 140 - 153
  • [2] Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates
    Chang, Zhengbo
    Meng, Xinzhu
    Lu, Xiao
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2017, 472 : 103 - 116
  • [3] The threshold of a stochastic SIRS epidemic model with saturated incidence
    Zhao, Yanan
    Jiang, Daqing
    APPLIED MATHEMATICS LETTERS, 2014, 34 : 90 - 93
  • [4] Threshold Behavior in a Class of Stochastic SIRS Epidemic Models With Nonlinear Incidence
    Tang, Tingting
    Teng, Zhidong
    Li, Zhiming
    STOCHASTIC ANALYSIS AND APPLICATIONS, 2015, 33 (06) : 994 - 1019
  • [5] Dynamics of a stochastic SIR epidemic model with saturated incidence
    Liu, Qun
    Chen, Qingmei
    APPLIED MATHEMATICS AND COMPUTATION, 2016, 282 : 155 - 166
  • [6] GLOBAL STABILITY FOR DELAY SIR AND SEIR EPIDEMIC MODELS WITH SATURATED INCIDENCE RATES
    Abta, Abdelhadi
    Kaddar, Abdelilah
    Alaoui, Hamad Talibi
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
  • [7] Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay
    Zhang, Hong
    Xia, Juan
    Georgescu, Paul
    NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2017, 22 (01): : 64 - 83
  • [8] Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination
    Wang, Lei
    Teng, Zhidong
    Tang, Tingting
    Li, Zhiming
    COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE, 2017, 2017
  • [9] A stochastic SIRS epidemic model with nonlinear incidence rate
    Cai, Yongli
    Kang, Yun
    Wang, Weiming
    APPLIED MATHEMATICS AND COMPUTATION, 2017, 305 : 221 - 240
  • [10] Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence
    Liu, Qun
    Jiang, Daqing
    Shi, Ningzhong
    Hayat, Tasawar
    Alsaedi, Ahmed
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2017, 469 : 510 - 517
12345