IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v188y2021icp509-536.html
   My bibliography  Save this article

Dynamic analysis of a fractional-order model for HIV with drug-resistance and CTL immune response

Author

Listed:
  • Shi, Ruiqing
  • Lu, Ting
  • Wang, Cuihong

Abstract

In this paper, a fractional-order model for HIV with drug-resistance and CTL immune response is established. Two cases (subsystem with drug-sensitive and subsystem with drug-resistant) are considered. For both subsystems: firstly, the existence and uniqueness of the positive solution is proved; secondly, the sufficient conditions for the stability of the disease-free equilibrium are obtained; finally, some numerical simulations are performed to verify the theoretical results. After that, the main system is analyzed in a similar way. Calculation indicates that the basic reproduction number of the main system is the maximum value of the basic reproduction numbers of the corresponding subsystems. In addition, through numerical simulation, we know that the drug efficacy plays an important role in the treatment of HIV.

Suggested Citation

  • Shi, Ruiqing & Lu, Ting & Wang, Cuihong, 2021. "Dynamic analysis of a fractional-order model for HIV with drug-resistance and CTL immune response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 509-536.
    • Handle: RePEc:eee:matcom:v:188:y:2021:i:c:p:509-536
    DOI: 10.1016/j.matcom.2021.04.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421001531
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.04.022?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. Juping Zhang & Yun Li & Zhen Jin & Huaiping Zhu, 2019. "Dynamics Analysis of an Avian Influenza A (H7N9) Epidemic Model with Vaccination and Seasonality," Complexity, Hindawi, vol. 2019, pages 1-15, March.
    2. Jun-Yuan Yang & Xiao-Yan Wang & Xue-Zhi Li, 2011. "Hopf Bifurcation for a Model of HIV Infection of C D 4 + T Cells with Virus Released Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-24, May.
    3. Pinto, Carla M.A. & Carvalho, Ana R.M., 2017. "The role of synaptic transmission in a HIV model with memory," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 76-95.
    4. Wang, Yan & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "A stochastic HIV infection model with T-cell proliferation and CTL immune response," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 477-493.
    5. Fathalla A. Rihan, 2013. "Numerical Modeling of Fractional-Order Biological Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, August.
    6. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
    7. Haokun Qi & Lidan Liu & Xinzhu Meng, 2017. "Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis," Complexity, Hindawi, vol. 2017, pages 1-14, November.
    8. Jiang, Xiaowu & Zhou, Xueyong & Shi, Xiangyun & Song, Xinyu, 2008. "Analysis of stability and Hopf bifurcation for a delay-differential equation model of HIV infection of CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 447-460.
    9. Lan, Guijie & Chen, Zhewen & Wei, Chunjin & Zhang, Shuwen, 2018. "Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 61-77.
    Full references (including those not matched with items on IDEAS)

    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. Arshad, Sadia & Defterli, Ozlem & Baleanu, Dumitru, 2020. "A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    2. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    3. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.
    4. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    5. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    6. Lei Fu & Hongwei Yang, 2019. "An Application of (3+1)-Dimensional Time-Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves," Complexity, Hindawi, vol. 2019, pages 1-15, August.
    7. Gafiychuk, V. & Datsko, B. & Meleshko, V., 2008. "Analysis of fractional order Bonhoeffer–van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 418-424.
    8. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    9. Ricardo Almeida & Agnieszka B. Malinowska & Tatiana Odzijewicz, 2019. "Optimal Leader–Follower Control for the Fractional Opinion Formation Model," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1171-1185, September.
    10. Rong Liu & Guirong Liu, 2018. "Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    11. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    12. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    13. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
    14. Selvan, T. Tamil & Kumar, M., 2023. "Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    15. Silva, Cristiana J. & Torres, Delfim F.M., 2019. "Stability of a fractional HIV/AIDS model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 180-190.
    16. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    17. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    18. Utsumi, Shinobu & Arefin, Md. Rajib & Tatsukawa, Yuichi & Tanimoto, Jun, 2022. "How and to what extent does the anti-social behavior of violating self-quarantine measures increase the spread of disease?," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    19. Zhang, Tongqian & Xu, Xinna & Wang, Xinzeng, 2023. "Dynamic analysis of a cytokine-enhanced viral infection model with time delays and CTL immune response," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    20. Zhu, Guanghu & Chen, Sixing & Shi, Benyun & Qiu, Hongjun & Xia, Shang, 2019. "Dynamics of echinococcosis transmission among multiple species and a case study in Xinjiang, China," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 103-109.

    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:188:y:2021:i:c:p:509-536. 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.