THE DYNAMIC BEHAVIOR OF DETERMINISTIC AND STOCHASTIC DELAYED SIQS MODEL

被引：16
作者：
Zhang, Xiaobing [1 ,2 ]
Huo, Haifeng [1 ,2 ]
Xiang, Hong [2 ]
Li, Dungang [2 ]
机构：
[1] Lanzhou Univ Technol, Coll Elect & Informat Engn, Lanzhou 730050, Gansu, Peoples R China
[2] Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Gansu, Peoples R China
来源：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2018年 / 8卷 / 04期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
Random perturbations; Ito's formula; the threshold; time delay; SIRS EPIDEMIC MODEL; STATIONARY DISTRIBUTION; QUARANTINE; STABILITY; THRESHOLD; EXTINCTION; OUTBREAK; SEIR;
D O I：
10.11948/2018.1061
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present the deterministic and stochastic delayed SIQS epidemic models. For the deterministic model, the basic reproductive number R-0 is given. Moreover, when R-0 < 1, the disease-free equilibrium is globally asymptotical stable. When R-0 > 1 and additional conditions hold, the endemic equilibrium is globally asymptotical stable. For the stochastic A model, a sharp threshold (R) over cap (0) which determines the extinction or persistence in the mean of the disease is presented. Sufficient conditions for extinction and persistence in the mean of the epidemic are established. Numerical simulations are also conducted in the analytic results.
引用
收藏
页码：1061 / 1084
页数：24
相关论文
共 44 条
  • [1] Stability of epidemic model with time delays influenced by stochastic perturbations
    Beretta, E
    Kolmanovskii, V
    Shaikhet, L
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 1998, 45 (3-4) : 269 - 277
  • [2] Geometric stability switch criteria in delay differential systems with delay dependent parameters
    Beretta, E
    Kuang, Y
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2002, 33 (05) : 1144 - 1165
  • [3] A stochastic SIRS epidemic model with infectious force under intervention strategies
    Cai, Yongli
    Kang, Yun
    Banerjee, Malay
    Wang, Weiming
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (12) : 7463 - 7502
  • [4] Chen X., 2016, NONLINEAR DYN, P1
  • [5] Model parameters and outbreak control for SARS
    Chowell, G
    Castillo-Chavez, C
    Fenimore, PW
    Kribs-Zaleta, CM
    Arriola, L
    Hyman, JM
    [J]. EMERGING INFECTIOUS DISEASES, 2004, 10 (07) : 1258 - 1263
  • [6] When is quarantine a useful control strategy for emerging infectious diseases?
    Day, T
    Park, A
    Madras, N
    Gumel, A
    Wu, JH
    [J]. AMERICAN JOURNAL OF EPIDEMIOLOGY, 2006, 163 (05) : 479 - 485
  • [7] Renaissance model of an epidemic with quarantine
    Dobay, Akos
    Gall, Gabriella E. C.
    Rankin, Daniel J.
    Bagheri, Homayoun C.
    [J]. JOURNAL OF THEORETICAL BIOLOGY, 2013, 317 : 348 - 358
  • [8] The concept of quarantine in history: from plague to SARS
    Gensini, GF
    Yacoub, MH
    Conti, AA
    [J]. JOURNAL OF INFECTION, 2004, 49 (04) : 257 - 261
  • [9] A STOCHASTIC DIFFERENTIAL EQUATION SIS EPIDEMIC MODEL
    Gray, A.
    Greenhalgh, D.
    Hu, L.
    Mao, X.
    Pan, J.
    [J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2011, 71 (03) : 876 - 902
  • [10] The SIS epidemic model with Markovian switching
    Gray, Alison
    Greenhalgh, David
    Mao, Xuerong
    Pan, Jiafeng
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 394 (02) : 496 - 516
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