IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v210y2024ics0167715224000786.html
   My bibliography  Save this article

SIR epidemic model with non-Lipschitz stochastic perturbations

Author

Listed:
  • Li, Shuang
  • Xiong, Jie

Abstract

This paper investigates a stochastic SIR epidemic model with non-Lipschitz coefficients in the diffusion term. Firstly, we study the existence and uniqueness of the global positive solution of this model. Then, we prove that the stochastic process has a stationary distribution, and we also establish an exact expression of the density function of the stationary distribution under certain parameter constraints. Finally, we discuss the extinction of the epidemic and the asymptotic properties around the equilibrium points of the deterministic SIR model.

Suggested Citation

  • Li, Shuang & Xiong, Jie, 2024. "SIR epidemic model with non-Lipschitz stochastic perturbations," Statistics & Probability Letters, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:stapro:v:210:y:2024:i:c:s0167715224000786
    DOI: 10.1016/j.spl.2024.110109
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224000786
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110109?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. Zhang, Tailei & Teng, Zhidong, 2008. "Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1456-1468.
    2. 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).
    3. 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.
    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. William Brock & Anastasios Xepapadeas, 2020. "The Economy, Climate Change and Infectious Diseases: Links and Policy Implications," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(4), pages 811-824, August.
    2. 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.
    3. 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.
    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. Raja Sekhara Rao, P. & Naresh Kumar, M., 2015. "A dynamic model for infectious diseases: The role of vaccination and treatment," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 34-49.
    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. Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    8. 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.
    9. Guo, Yingjia, 2017. "Stochastic regime switching SIR model driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 1-11.
    10. 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.
    11. Bobryk, R.V., 2021. "Stability analysis of a SIR epidemic model with random parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    12. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 870-882.
    13. Zhou, Yanli & Zhang, Weiguo, 2016. "Threshold of a stochastic SIR epidemic model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 204-216.
    14. 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.
    15. Cao, Zhongwei & Shi, Yuee & Wen, Xiangdan & Su, Huishuang & Li, Xue, 2020. "Dynamic behaviors of a two-group stochastic SIRS epidemic model with standard incidence rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    16. Chen, Shanshan & Jiang, Haijun & Li, Liang & Li, Jiarong, 2020. "Dynamical behaviors and optimal control of rumor propagation model with saturation incidence on heterogeneous networks," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    17. 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).
    18. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 816-826.
    19. Sabbar, Yassine, 2024. "Exploring threshold dynamics of a behavioral epidemic model featuring two susceptible classes and second-order jump–diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    20. Li, Li, 2015. "Patch invasion in a spatial epidemic model," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 342-349.

    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:stapro:v:210:y:2024:i:c:s0167715224000786. 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.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.