IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v618y2023ics037843712300256x.html
   My bibliography  Save this article

Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model

Author

Listed:
  • El Attouga, Sanae
  • Bouggar, Driss
  • El Fatini, Mohamed
  • Hilbert, Astrid
  • Pettersson, Roger

Abstract

A stochastic SIRS epidemic model with generalized nonlinear incidence and Lévy noise is investigated. First, we show the existence and uniqueness of a global positive solution. Then, we establish sufficient conditions for the extinction and persistence of the disease. The main results are proved under weak assumptions regarding the incidence function, the obtained results are proved under a Lévy-type perturbation without requiring the finiteness of its activity. Finally, numerical simulations are realized to illustrate the main results.

Suggested Citation

  • El Attouga, Sanae & Bouggar, Driss & El Fatini, Mohamed & Hilbert, Astrid & Pettersson, Roger, 2023. "Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    • Handle: RePEc:eee:phsmap:v:618:y:2023:i:c:s037843712300256x
    DOI: 10.1016/j.physa.2023.128701
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843712300256X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2023.128701?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. Wen, Buyu & Rifhat, Ramziya & Teng, Zhidong, 2019. "The stationary distribution in a stochastic SIS epidemic model with general nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 258-271.
    2. 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).
    3. Cao, Zhongwei & Shi, Yuee & Wen, Xiangdan & Liu, Liya & Hu, Jingwei, 2020. "Analysis of a hybrid switching SVIR epidemic model with vaccination and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(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. 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.
    6. 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).
    7. 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).
    8. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    9. De la Sen, M. & Alonso-Quesada, S. & Ibeas, A., 2015. "On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 953-976.
    Full references (including those not matched with items on IDEAS)

    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. 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).
    2. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    3. Liu, Songnan & Xu, Xiaojie & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of the DS-I-A model disease with periodic parameter function and Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 66-84.
    4. 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.
    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. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    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. 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.
    9. Yang, Bo, 2018. "A stochastic Feline immunodeficiency virus model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 448-458.
    10. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    11. Quan Wang & Li Zu & Daqing Jiang & Donal O’Regan, 2023. "Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching," Mathematics, MDPI, vol. 11(12), pages 1-17, June.
    12. Wei, Fengying & Chen, Fangxiang, 2016. "Stochastic permanence of an SIQS epidemic model with saturated incidence and independent random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 99-107.
    13. Boukanjime, Brahim & Caraballo, Tomás & El Fatini, Mohamed & El Khalifi, Mohamed, 2020. "Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Zhou, Baoquan & Zhang, Xinhong & Jiang, Daqing, 2020. "Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    15. Bao, Kangbo & Zhang, Qimin & Rong, Libin & Li, Xining, 2019. "Dynamics of an imprecise SIRS model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 489-506.
    16. Zhang, Xiao-Bing & Chang, Suqin & Shi, Qihong & Huo, Hai-Feng, 2018. "Qualitative study of a stochastic SIS epidemic model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 805-817.
    17. Tuerxun, Nafeisha & Wen, Buyu & Teng, Zhidong, 2021. "The stationary distribution in a class of stochastic SIRS epidemic models with non-monotonic incidence and degenerate diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 888-912.
    18. Saha, Sangeeta & Dutta, Protyusha & Samanta, Guruprasad, 2022. "Dynamical behavior of SIRS model incorporating government action and public response in presence of deterministic and fluctuating environments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    19. Zhang, Xinhong & Shi, Zhenfeng & Wang, Yuanyuan, 2019. "Dynamics of a stochastic avian–human influenza epidemic model with mutation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    20. Tong, Jinying & Zhang, Zhenzhong & Bao, Jianhai, 2013. "The stationary distribution of the facultative population model with a degenerate noise," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 655-664.

    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:phsmap:v:618:y:2023:i:c:s037843712300256x. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.