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The threshold of a stochastic delayed SIR epidemic model with vaccination

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  • Liu, Qun
  • Jiang, Daqing

Abstract

In this paper, we study the threshold dynamics of a stochastic delayed SIR epidemic model with vaccination. We obtain sufficient conditions for extinction and persistence in the mean of the epidemic. The threshold between persistence in the mean and extinction of the stochastic system is also obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R¯0 of the deterministic system. Results show that time delay has important effects on the persistence and extinction of the epidemic.

Suggested Citation

  • Liu, Qun & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 140-147.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:140-147
    DOI: 10.1016/j.physa.2016.05.036
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    References listed on IDEAS

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    Citations

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    Cited by:

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    5. Zhang, Xiao-Bing & Huo, Hai-Feng & Xiang, Hong & Shi, Qihong & Li, Dungang, 2017. "The threshold of a stochastic SIQS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 362-374.
    6. Chang, Zhengbo & Meng, Xinzhu & Lu, Xiao, 2017. "Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 103-116.
    7. Jia, Pingqi & Wang, Chao & Zhang, Gaoyu & Ma, Jianfeng, 2019. "A rumor spreading model based on two propagation channels in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 342-353.
    8. Li, Yan & Ye, Ming & Zhang, Qimin, 2019. "Strong convergence of the partially truncated Euler–Maruyama scheme for a stochastic age-structured SIR epidemic model," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    9. Verma, Tina & Gupta, Arvind Kumar, 2020. "Mean-field dispersal induced synchrony and stability in an epidemic model under patchy environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    10. M, Pitchaimani & M, Brasanna Devi, 2021. "Stochastic dynamical probes in a triple delayed SICR model with general incidence rate and immunization strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    11. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing, 2021. "Ergodic property, extinction and density function of a stochastic SIR epidemic model with nonlinear incidence and general stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. Wanduku, Divine, 2017. "Complete global analysis of a two-scale network SIRS epidemic dynamic model with distributed delay and random perturbations," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 49-76.
    13. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    14. Sharma, Natasha & Gupta, Arvind Kumar, 2017. "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 114-125.
    15. Xin, Ming-Zhen & Wang, Bin-Guo, 2020. "Stationary distribution and extinction of a stochastic tuberculosis model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    16. Jia, Fangju & Lv, Guangying, 2018. "Dynamic analysis of a stochastic rumor propagation model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 613-623.
    17. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    18. El Fatini, Mohamed & Sekkak, Idriss & Laaribi, Aziz, 2019. "A threshold of a delayed stochastic epidemic model with Crowly–Martin functional response and vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 151-160.
    19. Liu, Yue, 2022. "Extinction, persistence and density function analysis of a stochastic two-strain disease model with drug resistance mutation," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    20. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Wei, Xiang, 2017. "A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 198-208.
    21. Berrhazi, Badr-eddine & El Fatini, Mohamed & Laaribi, Aziz, 2018. "A stochastic threshold for an epidemic model with Beddington–DeAngelis incidence, delayed loss of immunity and Lévy noise perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 312-320.
    22. Nguyen, Dang H. & Nguyen, Nhu N. & Yin, George, 2021. "Stochastic functional Kolmogorov equations, I: Persistence," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 319-364.
    23. Hattaf, Khalid & Mahrouf, Marouane & Adnani, Jihad & Yousfi, Noura, 2018. "Qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 591-600.
    24. Huo, Liang'an & Ma, Chenyang, 2017. "Dynamical analysis of rumor spreading model with impulse vaccination and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 653-665.
    25. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.

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