IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v26y2005i3p947-958.html
   My bibliography  Save this article

A discrete epidemic model with stage structure

Author

Listed:
  • Li, Xiuying
  • Wang, Wendi

Abstract

A discrete SIS epidemic model with stage structure is proposed that a disease spreads among mature individuals. A basic reproduction number R0 of the model is formulated, which is more complicated to calculate than that of differential equation models because the attractor of the model in disease free space may compose of equilibria, period cycles, even strange attractors. If the recruitment rate is of Beverton–Holt type, when R0<1 and recovery rate is equal to 0, the disease free equilibrium is globally stable, and R0 is monotone for any parameter of the system. When the recruitment rate is of Richer’s type, it is shown that the existence and extinction of the disease can emerge alternately with the change of intrinsic growth rate. The method for finding basic reproduction number can be applied to other discrete epidemic models.

Suggested Citation

  • Li, Xiuying & Wang, Wendi, 2005. "A discrete epidemic model with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 947-958.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:3:p:947-958
    DOI: 10.1016/j.chaos.2005.01.063
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905001542
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.01.063?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Salman, S.M. & Ahmed, E., 2018. "A mathematical model for Creutzfeldt Jacob Disease (CJD)," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 249-260.
    2. 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.
    3. Pang, Guoping & Chen, Lansun, 2007. "A delayed SIRS epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1629-1635.
    4. 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.
    5. 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.
    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.
    7. 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.

    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:eee:chsofr:v:26:y:2005:i:3:p:947-958. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.