IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v137y2020ics0960077920302976.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920302976
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109897?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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).
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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).
    2. 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).
    3. Zhiming Li & Zhidong Teng, 2019. "Analysis of uncertain SIS epidemic model with nonlinear incidence and demography," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 475-491, December.
    4. Zhou, Yanli & Yuan, Sanling & Zhao, Dianli, 2016. "Threshold behavior of a stochastic SIS model with Le´vy jumps," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 255-267.
    5. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 58-69.
    6. Fu, Xiaoming, 2019. "On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1008-1023.
    7. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    8. Zhao, Dianli & Zhang, Tiansi & Yuan, Sanling, 2016. "The threshold of a stochastic SIVS epidemic model with nonlinear saturated incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 372-379.
    9. 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.
    10. Rifhat, Ramziya & Wang, Lei & Teng, Zhidong, 2017. "Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 176-190.
    11. El Fatini, M. & Taki, R. & Tridane, A., 2019. "Threshold behaviour of a stochastic epidemic model with two-dimensional noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 776-786.
    12. 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.
    13. 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).
    14. Berrhazi, Badreddine & El Fatini, Mohamed & Lahrouz, Aadil & Settati, Adel & Taki, Regragui, 2018. "A stochastic SIRS epidemic model with a general awareness-induced incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 968-980.
    15. 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).
    16. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li, 2019. "Dynamical behavior of a stochastic SEI epidemic model with saturation incidence and logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 894-907.
    17. 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.
    18. Cheng, Yingying & Huo, Liang’an & Zhao, Laijun, 2020. "Rumor spreading in complex networks under stochastic node activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    19. Shi, Zhenfeng & Zhang, Xinhong & Jiang, Daqing, 2019. "Dynamics of an avian influenza model with half-saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 399-416.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302976. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.