IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v271y2015icp716-729.html
   My bibliography  Save this article

Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination

Author

Listed:
  • Zhang, Tailei

Abstract

In this paper, by applying a nonstandard finite difference scheme, we formulate a discretized SIRVS epidemic model which takes into account vaccination. Under quite weak assumptions, the threshold value conditions on permanence and extinction of disease are established. Some new threshold values in product forms R0* and R1* are obtained. We show that the disease is permanent if R0*>1, and if R1*<1, then the disease is extinct. When the model degenerates into a periodic model, a sharp threshold value R0 is obtained for permanence versus extinction of disease. In order to illustrate our analytic analysis, some numerical simulations are also included in the end.

Suggested Citation

  • Zhang, Tailei, 2015. "Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 716-729.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:716-729
    DOI: 10.1016/j.amc.2015.09.071
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315013090
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.09.071?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. Li, Xiuying & Wang, Wendi, 2005. "A discrete epidemic model with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 947-958.
    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. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.
    2. De la Sen, M. & Alonso-Quesada, S. & Ibeas, A. & Nistal, R., 2019. "On an SEIADR epidemic model with vaccination, treatment and dead-infectious corpses removal controls," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 47-79.

    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. Pang, Guoping & Chen, Lansun, 2007. "A delayed SIRS epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1629-1635.
    2. Salman, S.M. & Ahmed, E., 2018. "A mathematical model for Creutzfeldt Jacob Disease (CJD)," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 249-260.
    3. Zhang, Tailei & Liu, Junli & Teng, Zhidong, 2009. "Bifurcation analysis of a delayed SIS epidemic model with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 563-576.
    4. Begoña Cantó & Carmen Coll & Maria Jesús Pagán & Joan Poveda & Elena Sánchez, 2021. "A Mathematical Model to Control the Prevalence of a Directly and Indirectly Transmitted Disease," Mathematics, MDPI, vol. 9(20), pages 1-15, October.
    5. Yang, Junyuan & Zhang, Fengqin & Li, Xuezhi, 2009. "Epidemic model with vaccinated age that exhibits backward bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1721-1731.
    6. Jin, Yu & Wang, Wendi & Xiao, Shiwu, 2007. "An SIRS model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1482-1497.

    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:apmaco:v:271:y:2015:i:c:p:716-729. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.