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Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel

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  • Caraballo, Tomás
  • Fatini, Mohamed El
  • Khalifi, Mohamed El
  • Gerlach, Richard
  • Pettersson, Roger

Abstract

In this work, we investigate a stochastic epidemic model with relapse and distributed delay. First, we prove that our model possesses and unique global positive solution. Next, by means of the Lyapunov method, we determine some sufficient criteria for the extinction of the disease and its persistence. In addition, we establish the existence of a unique stationary distribution to our model. Finally, we provide some numerical simulations for the stochastic model to assist and show the applicability and efficiency of our results.

Suggested Citation

  • Caraballo, Tomás & Fatini, Mohamed El & Khalifi, Mohamed El & Gerlach, Richard & Pettersson, Roger, 2020. "Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300424
    DOI: 10.1016/j.chaos.2020.109643
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    1. El Fatini, Mohamed & El Khalifi, Mohamed & Gerlach, Richard & Laaribi, Aziz & Taki, Regragui, 2019. "Stationary distribution and threshold dynamics of a stochastic SIRS model with a general incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. Xu, Changyong & Li, Xiaoyue, 2018. "The threshold of a stochastic delayed SIRS epidemic model with temporary immunity and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 227-234.
    3. Lu, Qiuying, 2009. "Stability of SIRS system with random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3677-3686.
    4. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold dynamics of a stochastic SIS epidemic model with nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    5. 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.
    6. 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.
    7. 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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    Cited by:

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    3. Laaribi, Aziz & Boukanjime, Brahim & El Khalifi, Mohamed & Bouggar, Driss & El Fatini, Mohamed, 2023. "A generalized stochastic SIRS epidemic model incorporating mean-reverting Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
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    5. Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution and extinction of a stochastic staged progression AIDS model with staged treatment and second-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    7. 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).
    8. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    10. Settati, A. & Lahrouz, A. & Assadouq, A. & El Fatini, M. & El Jarroudi, M. & Wang, K., 2020. "The impact of nonlinear relapse and reinfection to derive a stochastic threshold for SIRI epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).

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