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Nonlinear Dynamics and Chaos in a Fractional-Order HIV Model

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  • Haiping Ye
  • Yongsheng Ding

Abstract

We introduce fractional order into an HIV model. We consider the effect of viral diversity on the human immune system with frequency dependent rate of proliferation of cytotoxic T-lymphocytes (CTLs) and rate of elimination of infected cells by CTLs, based on a fractional-order differential equation model. For the one-virus model, our analysis shows that the interior equilibrium which is unstable in the classical integer-order model can become asymptotically stable in our fractional-order model and numerical simulations confirm this. We also present simulation results of the chaotic behaviors produced from the fractional-order HIV model with viral diversity by using an Adams-type predictor-corrector method.

Suggested Citation

  • Haiping Ye & Yongsheng Ding, 2009. "Nonlinear Dynamics and Chaos in a Fractional-Order HIV Model," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-12, June.
    • Handle: RePEc:hin:jnlmpe:378614
    DOI: 10.1155/2009/378614
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    Cited by:

    1. Yadav, Ram Prasad & Renu Verma,, 2020. "A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Mekoth, Chitra & George, Santhosh & Jidesh, P., 2021. "Fractional Tikhonov regularization method in Hilbert scales," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Fu, Peng & Wang, Can-Jun & Yang, Ke-Li & Li, Xu-Bo & Yu, Biao, 2022. "Reentrance-like vibrational resonance in a fractional-order birhythmic biological system," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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