IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2013y2013i1n154387.html

Dynamical Analysis of SIR Epidemic Models with Distributed Delay

Author

Listed:
  • Wencai Zhao
  • Tongqian Zhang
  • Zhengbo Chang
  • Xinzhu Meng
  • Yulin Liu

Abstract

SIR epidemic models with distributed delay are proposed. Firstly, the dynamical behaviors of the model without vaccination are studied. Using the Jacobian matrix, the stability of the equilibrium points of the system without vaccination is analyzed. The basic reproduction number R is got. In order to study the important role of vaccination to prevent diseases, the model with distributed delay under impulsive vaccination is formulated. And the sufficient conditions of globally asymptotic stability of “infection‐free” periodic solution and the permanence of the model are obtained by using Floquet’s theorem, small‐amplitude perturbation skills, and comparison theorem. Lastly, numerical simulation is presented to illustrate our main conclusions that vaccination has significant effects on the dynamical behaviors of the model. The results can provide effective tactic basis for the practical infectious disease prevention.

Suggested Citation

  • Wencai Zhao & Tongqian Zhang & Zhengbo Chang & Xinzhu Meng & Yulin Liu, 2013. "Dynamical Analysis of SIR Epidemic Models with Distributed Delay," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:154387
    DOI: 10.1155/2013/154387
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/154387
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/154387?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
    ---><---

    References listed on IDEAS

    as
    1. Gao, Shujing & Teng, Zhidong & Xie, Dehui, 2009. "Analysis of a delayed SIR epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1004-1011.
    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. Christou, Katerina, 2026. "The numerical solution of epidemic models on moving domains using combined masses," Applied Mathematics and Computation, Elsevier, vol. 509(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. Dong, Yafang & Huo, Liang'an & Zhao, Laijun, 2022. "An improved two-layer model for rumor propagation considering time delay and event-triggered impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Imane Abouelkheir & Fadwa El Kihal & Mostafa Rachik & Ilias Elmouki, 2019. "Optimal Impulse Vaccination Approach for an SIR Control Model with Short-Term Immunity," Mathematics, MDPI, vol. 7(5), pages 1-21, May.
    3. Awawdeh, Fadi & Adawi, A. & Mustafa, Z., 2009. "Solutions of the SIR models of epidemics using HAM," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3047-3052.
    4. Alrebdi, H.I. & Steklain, Andre & Amorim, Edgard P.M. & Zotos, Euaggelos, 2023. "Thermostated Susceptible-Infected-Susceptible epidemic model," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    5. John C. Eckalbar & Pete Tsournos & Walter L. Eckalbar, 2015. "Dynamics In An Sir Model When Vaccination Demand Follows Prior Levels Of Disease Prevalence," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 18(07n08), pages 1-27, November.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnljam:v:2013:y:2013:i:1:n:154387. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.