IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v128y2016icp26-41.html
   My bibliography  Save this article

Stability and Hopf bifurcation in a HIV-1 infection model with delays and logistic growth

Author

Listed:
  • Hu, Qing
  • Hu, Zhixing
  • Liao, Fucheng

Abstract

In this paper, we consider the dynamical behavior of a HIV-1 infection model with logistic growth for target cells, time delay and two predominant infection modes, namely the classical cell-free infection and the direct cell-to-cell transfer. It is proved the existence of the positive equilibrium E2 in different conditions. By analyzing the characteristic equations and using stability theory of delay differential equations, we establish the local stability of the two boundary equilibria and the infected equilibrium of the model. The time delay does not affect the stability of the boundary equilibrium, but can change the stability of E2 and lead to the occurrence of Hopf bifurcations. The direction and stability of bifurcating periodic solutions is also studied. Finally, the numerical simulations are carried out to explain our theorems.

Suggested Citation

  • Hu, Qing & Hu, Zhixing & Liao, Fucheng, 2016. "Stability and Hopf bifurcation in a HIV-1 infection model with delays and logistic growth," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 26-41.
    • Handle: RePEc:eee:matcom:v:128:y:2016:i:c:p:26-41
    DOI: 10.1016/j.matcom.2016.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475416300325
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2016.04.003?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. Avila-Vales, Eric & Chan-Chí, Noé & García-Almeida, Gerardo E. & Vargas-De-León, Cruz, 2015. "Stability and Hopf bifurcation in a delayed viral infection model with mitosis transmission," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 293-312.
    2. Dong, Yueping & Huang, Gang & Miyazaki, Rinko & Takeuchi, Yasuhiro, 2015. "Dynamics in a tumor immune system with time delays," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 99-113.
    3. 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.
    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. Sonjoy Pan & Siddhartha P. Chakrabarty, 2020. "Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1673-1695, December.
    2. Pan, Sonjoy & Chakrabarty, Siddhartha P., 2022. "Analysis of a reaction–diffusion HCV model with general cell-to-cell incidence function incorporating B cell activation and cure rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 431-450.

    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, Xiangdong & Li, Qingze & Pan, Jianxin, 2018. "A deterministic and stochastic model for the system dynamics of tumor–immune responses to chemotherapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 162-176.
    2. Wang, Jinliang & Guo, Min & Liu, Xianning & Zhao, Zhitao, 2016. "Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 149-161.
    3. Dzyubak, Larysa & Dzyubak, Oleksandr & Awrejcewicz, Jan, 2023. "Nonlinear multiscale diffusion cancer invasion model with memory of states," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Barman, Madhab & Mishra, Nachiketa, 2024. "Hopf bifurcation analysis for a delayed nonlinear-SEIR epidemic model on networks," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Jiao, Xubin & Liu, Xiuxiang, 2024. "Rich dynamics of a delayed Filippov avian-only influenza model with two-thresholds policy," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    6. Duan, Wei-Long & Lin, Ling, 2021. "Noise and delay enhanced stability in tumor-immune responses to chemotherapy system," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    7. Yi Xie & Ziheng Zhang & Yan Wu & Shuang Li & Liuyong Pang & Yong Li, 2024. "Time-Delay Dynamic Model and Cost-Effectiveness Analysis of Major Emergent Infectious Diseases with Transportation-Related Infection and Entry-Exit Screening," Mathematics, MDPI, vol. 12(13), pages 1-25, July.
    8. Rihan, F.A. & Velmurugan, G., 2020. "Dynamics of fractional-order delay differential model for tumor-immune system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    9. Hyukpyo Hong & Eunjin Eom & Hyojung Lee & Sunhwa Choi & Boseung Choi & Jae Kyoung Kim, 2024. "Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    10. Dehingia, Kaushik & Das, Parthasakha & Upadhyay, Ranjit Kumar & Misra, Arvind Kumar & Rihan, Fathalla A. & Hosseini, Kamyar, 2023. "Modelling and analysis of delayed tumour–immune system with hunting T-cells," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 669-684.
    11. Li, Jianquan & Xie, Xin & Chen, Yuming & Zhang, Dian, 2021. "Complex dynamics of a tumor-immune system with antigenicity," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    12. Michail P. Markakis & Panagiotis S. Douris, 2016. "On the Computation of Degenerate Hopf Bifurcations for -Dimensional Multiparameter Vector Fields," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-12, June.
    13. Xu, Rui & Wang, Zhili & Zhang, Fengqin, 2015. "Global stability and Hopf bifurcations of an SEIR epidemiological model with logistic growth and time delay," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 332-342.

    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:matcom:v:128:y:2016:i:c:p:26-41. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.