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A stochastic threshold for an epidemic model with Beddington–DeAngelis incidence, delayed loss of immunity and Lévy noise perturbation

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  • Berrhazi, Badr-eddine
  • El Fatini, Mohamed
  • Laaribi, Aziz

Abstract

In this paper we study a stochastic epidemic model with delayed loss of immunity and Lévy noise perturbation. We establish the uniqueness of the global positive solution. We also investigate the extinction and the persistence in mean of the disease.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:507:y:2018:i:c:p:312-320
    DOI: 10.1016/j.physa.2018.05.096
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    References listed on IDEAS

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    1. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 767-777.
    2. El Fatini, Mohamed & Lahrouz, Aadil & Pettersson, Roger & Settati, Adel & Taki, Regragui, 2018. "Stochastic stability and instability of an epidemic model with relapse," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 326-341.
    3. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar, 2018. "Dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2010-2018.
    4. 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.
    5. Liu, Qun & Chen, Qingmei & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 115-125.
    6. 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.
    7. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
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    Citations

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    Cited by:

    1. El Fatini, Mohamed & Sekkak, Idriss, 2020. "Lévy noise impact on a stochastic delayed epidemic model with Crowly–Martin incidence and crowding effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    2. 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.
    3. Liu, Fangfang & Wei, Fengying, 2022. "An epidemic model with Beddington–DeAngelis functional response and environmental fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    4. Yang, Ying & Zhang, Jingwen & Wang, Kaiyuan & Zhang, Guofang, 2024. "Stationary distribution, density function and extinction of a stochastic SIQR epidemic model with Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    5. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Chen, Shihua, 2020. "A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    6. Caraballo, Tomás & Settati, Adel & Fatini, Mohamed El & Lahrouz, Aadil & Imlahi, Abdelouahid, 2019. "Global stability and positive recurrence of a stochastic SIS model with Lévy noise perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 677-690.
    7. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    8. Berrhazi, Badr-eddine & El Fatini, Mohamed & Laaribi, Aziz & Pettersson, Roger, 2018. "A stochastic viral infection model driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 446-452.

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