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A stochastic SIRS epidemic model incorporating media coverage and driven by Lévy noise

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  • Berrhazi, Badr-eddine
  • El Fatini, Mohamed
  • Laaribi, Aziz
  • Pettersson, Roger
  • Taki, Regragui

Abstract

In this paper, we establish the existence of a unique global positive solution for a stochastic epidemic model, incorporating media coverage and driven by Lévy noise. We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we present some numerical results to support the theoretical work.

Suggested Citation

  • Berrhazi, Badr-eddine & El Fatini, Mohamed & Laaribi, Aziz & Pettersson, Roger & Taki, Regragui, 2017. "A stochastic SIRS epidemic model incorporating media coverage and driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 60-68.
    • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:60-68
    DOI: 10.1016/j.chaos.2017.10.007
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    References listed on IDEAS

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    1. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    2. Zhao, Yanan & Jiang, Daqing & O’Regan, Donal, 2013. "The extinction and persistence of the stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4916-4927.
    3. Liu, Wenbin & Zheng, Qiben, 2015. "A stochastic SIS epidemic model incorporating media coverage in a two patch setting," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 160-168.
    4. 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.
    5. 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.
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    Citations

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    Cited by:

    1. Chen, Xingzhi & Xu, Xin & Tian, Baodan & Li, Dong & Yang, Dan, 2022. "Dynamics of a stochastic delayed chemostat model with nutrient storage and Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    2. Liu, Chao & Tian, Yilin & Chen, Peng & Cheung, Lora, 2024. "Stochastic dynamic effects of media coverage and incubation on a distributed delayed epidemic system with Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    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. 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).
    5. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2024. "A novel SIRS epidemic model for two diseases incorporating treatment functions, media coverage, and three types of noise," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    6. 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.
    7. Liu, Xiaohua & Li, Mengling & Zeng, Pengyu, 2024. "Adaptive finite-time neural network control for nonlinear stochastic systems with state constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 82-97.

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