IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v30y2006i1p204-216.html
   My bibliography  Save this article

Stability and Hopf bifurcation for an epidemic disease model with delay

Author

Listed:
  • Sun, Chengjun
  • Lin, Yiping
  • Han, Maoan

Abstract

A predator–prey system with disease in the prey is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation with delay τ in the term of degree 2 is investigated, where τ is regarded as a parameter. It is found that there are stability switches, and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, direction and other properties of bifurcating periodic solutions is derived.

Suggested Citation

  • Sun, Chengjun & Lin, Yiping & Han, Maoan, 2006. "Stability and Hopf bifurcation for an epidemic disease model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 204-216.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:1:p:204-216
    DOI: 10.1016/j.chaos.2005.08.167
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905008003
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.08.167?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. Yang, Hong-Yong & Tian, Yu-Ping, 2005. "Hopf bifurcation in REM algorithm with communication delay," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1093-1105.
    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. Zhao, Huitao & Lin, Yiping, 2009. "Hopf bifurcation in a partial dependent predator–prey system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 896-900.
    2. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    3. Li, Xue-Zhi & Li, Wen-Sheng & Ghosh, Mini, 2009. "Stability and bifurcation of an SIS epidemic model with treatment," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2822-2832.
    4. Nasir, Hanis, 2022. "On the dynamics of a diabetic population model with two delays and a general recovery rate of complications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 571-602.
    5. Liu, Junli & Zhang, Tailei, 2009. "Bifurcation analysis of an SIS epidemic model with nonlinear birth rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1091-1099.
    6. Zhang, Xue & Zhang, Qing-ling & Zhang, Yue, 2009. "Bifurcations of a class of singular biological economic models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1309-1318.
    7. Tipsri, S. & Chinviriyasit, W., 2015. "The effect of time delay on the dynamics of an SEIR model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 153-172.
    8. Poria, Swarup & Poria, Anindita Tarai & Chatterjee, Prasanta, 2009. "Synchronization threshold of a coupled n-dimensional time-delay system," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1123-1124.
    9. Hu, Guang-Ping & Li, Xiao-Ling, 2012. "Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 229-237.
    10. Gan, Qintao & Xu, Rui & Yang, Pinghua, 2009. "Bifurcation and chaos in a ratio-dependent predator–prey system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1883-1895.
    11. Jingyi Zhao & Chunhai Gao & Tao Tang, 2022. "A Review of Sustainable Maintenance Strategies for Single Component and Multicomponent Equipment," Sustainability, MDPI, vol. 14(5), pages 1-22, March.

    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. Wang, Xia & Tao, Youde & Song, Xinyu, 2009. "Stability and Hopf bifurcation on a model for HIV infection of CD4+ T cells with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1838-1844.
    2. Liu, Junli & Zhang, Tailei, 2009. "Bifurcation analysis of an SIS epidemic model with nonlinear birth rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1091-1099.
    3. Chen, Yuanyuan & Yu, Jiang & Sun, Chengjun, 2007. "Stability and Hopf bifurcation analysis in a three-level food chain system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 683-694.
    4. Nga, J.H.C. & Iu, H.H.C. & Ling, S.H. & Lam, H.K., 2008. "Comparative study of stability in different TCP/RED models," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 977-987.
    5. Sun, Chengjun & Lin, Yiping & Han, Maoan & Tang, Shoupeng, 2007. "Analysis for a special first order characteristic equation with delay dependent parameters," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 388-395.
    6. Sun, Chengjun & Cao, Zhijie & Lin, Yiping, 2007. "Analysis of stability and Hopf bifurcation for a viral infectious model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 234-245.
    7. Liu, Cheng-Lin & Tian, Yu-Ping, 2008. "Eliminating oscillations in the Internet by time-delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 878-887.
    8. Chen, Chang-Kuo & Liao, Teh-Lu & Yan, Jun-Juh, 2009. "Active queue management controller design for TCP communication networks: Variable structure control approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 277-285.
    9. Ge, Zheng-Ming & Zhang, An-Ray, 2007. "Chaos in a modified van der Pol system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1791-1822.
    10. Hu, H.Y. & Wang, Z.H., 2009. "Singular perturbation methods for nonlinear dynamic systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 13-27.
    11. 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.

    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:30:y:2006:i:1:p:204-216. 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: 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.