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The impact of nonlinear relapse and reinfection to derive a stochastic threshold for SIRI epidemic model

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  • Settati, A.
  • Lahrouz, A.
  • Assadouq, A.
  • El Fatini, M.
  • El Jarroudi, M.
  • Wang, K.

Abstract

In the present work, we introduce a stochastic SIRI epidemic model with nonlinear relapse. We give sufficient conditions for extinction and persistence of the disease. We also study the existence of a stationary distribution and the ergodicity of the solutions. As a special case of our results that under some conditions on noise intensities, we obtain the threshold Rβ for the disease. Finally, we provide some computer simulations to illustrate our theoretical findings.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302976
    DOI: 10.1016/j.chaos.2020.109897
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    References listed on IDEAS

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    1. Peiyan Xia & Xiaokun Zheng & Daqing Jiang, 2013. "Persistence and Nonpersistence of a Nonautonomous Stochastic Mutualism System," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, February.
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Stationary distribution of a stochastic delayed SVEIR epidemic model with vaccination and saturation incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 849-863.
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    1. Settati, A. & Lahrouz, A. & Zahri, M. & Tridane, A. & El Fatini, M. & El Mahjour, H. & Seaid, M., 2021. "A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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