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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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