IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v520y2019icp489-506.html
   My bibliography  Save this article

Dynamics of an imprecise SIRS model with Lévy jumps

Author

Listed:
  • Bao, Kangbo
  • Zhang, Qimin
  • Rong, Libin
  • Li, Xining

Abstract

Sudden environmental perturbations may affect population dynamics. Parameters of mathematical models can also be imprecise due to uncertainties and unknown data. How sudden environmental noise and parameter imprecision influence the dynamics of epidemic systems remains unclear. This paper studies a stochastic Susceptible–Infected–Recovered–Susceptible (SIRS) model that includes Lévy jumps and interval parameters. We prove that the model has a unique global positive solution. Sufficient conditions for persistence and extinction of the disease are obtained. Large noise intensity is able to suppress the emergence of disease outbreaks. Numerical simulations are carried out to show the influence of stochastic noise on disease dynamics. These results suggest that Lévy jumps and imprecise parameters can greatly affect the long-term behavior of the epidemic system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:520:y:2019:i:c:p:489-506
    DOI: 10.1016/j.physa.2019.01.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119300275
    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.2019.01.027?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. Lin, Yuguo & Jiang, Daqing & Wang, Shuai, 2014. "Stationary distribution of a stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 187-197.
    2. 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.
    3. 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.
    4. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    5. Wang, Weiming & Cai, Yongli & Ding, Zuqin & Gui, Zhanji, 2018. "A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 921-936.
    6. 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.
    7. 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.
    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. Liu, Chao & Tian, Yilin & Chen, Peng & Cheung, Lora, 2024. "Stochastic dynamic effects of media coverage and incubation on a distributed delayed epidemic system with Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. 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).

    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. 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.
    2. 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.
    3. 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.
    4. Han, Cheng & Wang, Yan & Jiang, Daqing, 2023. "Dynamics analysis of a stochastic HIV model with non-cytolytic cure and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    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. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 767-777.
    7. 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).
    8. 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.
    9. Lan, Guijie & Chen, Zhewen & Wei, Chunjin & Zhang, Shuwen, 2018. "Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 61-77.
    10. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
    11. 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.
    12. 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.
    13. 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).
    14. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    15. 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.
    16. 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).
    17. Liu, Qun & Jiang, Daqing, 2020. "Stationary distribution of a stochastic cholera model with imperfect vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    18. 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).
    19. 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.
    20. Huo, Hai-Feng & Jing, Shuang-Lin & Wang, Xun-Yang & Xiang, Hong, 2020. "Modeling and analysis of a H1N1 model with relapse and effect of Twitter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).

    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:520:y:2019:i:c:p:489-506. 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.