IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i3p1838-1844.html
   My bibliography  Save this article

Stability and Hopf bifurcation on a model for HIV infection of CD4+ T cells with delay

Author

Listed:
  • Wang, Xia
  • Tao, Youde
  • Song, Xinyu

Abstract

In this paper, a delayed differential equation model that describes HIV infection of CD4+ T cells is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1838-1844
    DOI: 10.1016/j.chaos.2009.03.089
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909002094
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.03.089?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.
    2. Jerome K. Percus & Ora E. Percus & Alan S. Perelson, 1993. "Predicting the Size of the T-Cell Receptor and Antibody Combining Region from Consideration of Efficient Self-Nonself Discrimination," Working Papers 93-04-019, Santa Fe Institute.
    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. Tanvi, & Aggarwal, Rajiv, 2020. "Stability analysis of a delayed HIV-TB co-infection model in resource limitation settings," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Jajarmi, Amin & Baleanu, Dumitru, 2018. "A new fractional analysis on the interaction of HIV with CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 221-229.

    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. 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.
    2. 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.
    3. Derek J. Smith & Stephanie Forrest & Ron R. Hightower & Alan S. Perelson, 1997. "Deriving Shape Space Parameters from Immunological Data for a Model of Cross-Reactive Memory," Working Papers 97-03-017, Santa Fe Institute.
    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. Cheng, Yan & Li, Mingtao & Zhang, Fumin, 2019. "A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 62-70.
    9. 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.
    10. 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.
    11. 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.
    12. Huang, Zaitang & Yang, Qigui & Cao, Junfei, 2011. "Complex dynamics in a stochastic internal HIV model," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 954-963.
    13. 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.
    14. 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.

    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:42:y:2009:i:3:p:1838-1844. 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.