IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i2p215-d1315800.html
   My bibliography  Save this article

SIR Epidemic Model with General Nonlinear Incidence Rate and Lévy Jumps

Author

Listed:
  • Shuang Li

    (Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, China)

Abstract

This article proposes a stochastic SIR model with general nonlinear incidence and Lévy jumps, which is used to describe diseases spreading in human populations. The model takes into account the randomness and sublinearity of diseases and can more accurately describe the disease transmission process. Firstly, we prove that this stochastic SIR model has a unique global positive solution. Then, sufficient conditions for the extinction of the disease are given. We also discuss the case that the disease persists in the model. In addition, we study the asymptotic behavior of the solution of the stochastic SIR model relative to the equilibrium points of the deterministic SIR model. These results allow us to understand the trends and dynamic changes of diseases in human populations, providing theoretical support for developing more scientific and effective disease control strategies and prevention measures. Finally, we give some examples and numerical simulations to demonstrate the effectiveness and feasibility of the theoretical results.

Suggested Citation

  • Shuang Li, 2024. "SIR Epidemic Model with General Nonlinear Incidence Rate and Lévy Jumps," Mathematics, MDPI, vol. 12(2), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:215-:d:1315800
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/2/215/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/2/215/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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).
    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).
    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. Huyi Wang & Ge Zhang & Tao Chen & Zhiming Li, 2023. "Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence," Mathematics, MDPI, vol. 11(7), pages 1-17, April.
    2. Zhang, Yuexia & Pan, Dawei, 2021. "Layered SIRS model of information spread in complex networks," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Han, Bingtao & Jiang, Daqing & Zhou, Baoquan & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Liu, Qun & Jiang, Daqing, 2023. "Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus (COVID-19) with asymptomatic carriers," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Yousef Alnafisah & Moustafa El-Shahed, 2022. "Stochastic Analysis of a Hantavirus Infection Model," Mathematics, MDPI, vol. 10(20), pages 1-15, October.

    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:gam:jmathe:v:12:y:2024:i:2:p:215-:d:1315800. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.