IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v113y2018icp221-229.html
   My bibliography  Save this article

A new fractional analysis on the interaction of HIV with CD4+ T-cells

Author

Listed:
  • Jajarmi, Amin
  • Baleanu, Dumitru

Abstract

Mathematical modeling of biological systems is an interesting research topic that attracted the attention of many researchers. One of the main goals in this area is the design of mathematical models that more accurately illustrate the characteristics of the real-world phenomena. Among the existing research projects, modeling of immune systems has given a growing attention due to its natural capabilities in identifying and destroying abnormal cells. The main objective of this paper is to investigate the pathological behavior of HIV-infection using a new model in fractional calculus. The proposed model is examined through three different operators of fractional derivatives. An efficient numerical method is also presented to solve these fractional models effectively. In fact, we believe that the new models presented on the basis of these three operators show various asymptomatic behaviors that do not appear during the modeling with the integer-order derivatives. Therefore, the fractional calculus provides more precise models of biological systems that help us to make more realistic judgments about their complex dynamics. Finally, simulations results are provided to confirm the theoretical analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:221-229
    DOI: 10.1016/j.chaos.2018.06.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918303825
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.06.009?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. 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. Cai, Liming & Li, Xuezhi, 2009. "Stability and Hopf bifurcation in a delayed model for HIV infection of CD4+T cells," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 1-11.
    3. Yan, Ye & Kou, Chunhai, 2012. "Stability analysis for a fractional differential model of HIV infection of CD4+ T-cells with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1572-1585.
    4. Moustafa, Mahmoud & Mohd, Mohd Hafiz & Ismail, Ahmad Izani & Abdullah, Farah Aini, 2018. "Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 1-13.
    5. Dehghan, Mehdi & Nasri, Mostafa & Razvan, Mohammad Reza, 2007. "Global stability of a deterministic model for HIV infection in vivo," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1225-1238.
    6. 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.
    7. Ma, Yong-Ki & Prakash, P. & Deiveegan, A., 2018. "Generalized Tikhonov methods for an inverse source problem of the time-fractional diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 39-48.
    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. Zhang, Huaqiao & Chen, Hong & Jiang, Cuicui & Wang, Kaifa, 2017. "Effect of explicit dynamics of free virus and intracellular delay," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 827-834.
    2. 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).
    3. Bai, Ning & Xu, Rui, 2022. "Backward bifurcation and stability analysis in a within-host HIV model with both virus-to-cell infection and cell-to-cell transmission, and anti-retroviral therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 162-185.
    4. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
    5. Aliyu, Murtala Bello & Mohd, Mohd Hafiz, 2021. "The interplay between mutualism, competition and dispersal promotes species coexistence in a multiple interactions type system," Ecological Modelling, Elsevier, vol. 452(C).
    6. Konstantin E. Starkov & Anatoly N. Kanatnikov, 2021. "Eradication Conditions of Infected Cell Populations in the 7-Order HIV Model with Viral Mutations and Related Results," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    7. Trong, Dang Duc & Hai, Dinh Nguyen Duy & Minh, Nguyen Dang, 2020. "Reconstruction of a space-dependent source in the inexact order time-fractional diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Zhao, Jingjun & Jiang, Xingzhou & Xu, Yang, 2021. "Generalized Adams method for solving fractional delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 401-419.
    9. Hao, Zhaopeng & Fan, Kai & Cao, Wanrong & Sun, Zhizhong, 2016. "A finite difference scheme for semilinear space-fractional diffusion equations with time delay," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 238-254.
    10. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Zhang, Minsong & Ding, Ling & Cao, Jinde & Alsaedi, Ahmed, 2020. "Dynamic optimal control of enhancing feedback treatment for a delayed fractional order predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    11. Jun Lu & Lianpeng Shi & Chein-Shan Liu & C. S. Chen, 2022. "Solving Inverse Conductivity Problems in Doubly Connected Domains by the Homogenization Functions of Two Parameters," Mathematics, MDPI, vol. 10(13), pages 1-17, June.
    12. Li, Dongfang & Zhang, Chengjian, 2020. "Long time numerical behaviors of fractional pantograph equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 244-257.
    13. Uddin, Md. Jasim & Rana, Sarker Md. Sohel & Işık, Seval & Kangalgil, Figen, 2023. "On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    14. Chunning Song & Yu Zhang & Qijin Ling & Shaogeng Zheng, 2022. "Joint Estimation of SOC and SOH for Single-Flow Zinc–Nickel Batteries," Energies, MDPI, vol. 15(13), pages 1-16, June.
    15. Yingkang Xie & Zhen Wang & Bo Meng, 2019. "Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    16. Songshu Liu, 2022. "Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
    17. Agus Suryanto & Isnani Darti & Hasan S. Panigoro & Adem Kilicman, 2019. "A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting," Mathematics, MDPI, vol. 7(11), pages 1-13, November.
    18. Yao, Zichen & Yang, Zhanwen & Gao, Jianfang, 2023. "Unconditional stability analysis of Grünwald Letnikov method for fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    19. Mohd, Mohd Hafiz & Md. Noorani, Mohd Salmi, 2021. "Local dispersal, trophic interactions and handling times mediate contrasting effects in prey-predator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    20. Cai, Liming & Li, Xuezhi, 2009. "Stability and Hopf bifurcation in a delayed model for HIV infection of CD4+T cells," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 1-11.

    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:113:y:2018:i:c:p:221-229. 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.