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Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order

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  • Naik, Parvaiz Ahmad
  • Zu, Jian
  • Owolabi, Kolade M.

Abstract

In this paper, we propose and analyze a fractional order model of viral kinetics for primary infection of HIV-1 in presence of immune control with treatment, as the classical model of target-cell-limited model is unable to predict long term viral kinetics unless a delayed immune effect is assumed. Further, the reverse transcriptase treatment can be incorporated by reducing the target cell infection rate. The existence of equilibria and their asymptotical stability results using fractional Routh–Hurwitz stability criterion will be discussed. A threshold value ′R0′ known as basic reproduction number has been found to ensure the extinction or persistence of the infection. The numerical solution using generalized Adams–Bashforth–Moulton method to the proposed HIV-1 fractional model is obtained. Also, the sufficient conditions that guarantee the asymptotic stability of endemic equilibrium point is presented. Meanwhile, global asymptotic stability of the endemic equilibrium point is investigated by constructing a suitable Lyapunov functions. The fractional derivative is described in Caputo sense. The obtained numerical results of the proposed model show the effectiveness and strength of the Adams–Bashforth–Moulton method. Some numerical simulations are given to illustrate the analytical results.

Suggested Citation

  • Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321235
    DOI: 10.1016/j.physa.2019.123816
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    References listed on IDEAS

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    1. Dubey, Preeti & Dubey, Uma S. & Dubey, Balram, 2018. "Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 120-137.
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    7. Owolabi, Kolade M., 2019. "Mathematical modelling and analysis of love dynamics: A fractional approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 849-865.
    8. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    9. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
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    Cited by:

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    9. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
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    More about this item

    Keywords

    HIV virus; Primary infection; Caputo fractional derivative; Immune response; Reverse transcriptase treatment; Adams–Bashforth–Moulton method; Stability analysis; Reproduction number R0;
    All these keywords.

    JEL classification:

    • R0 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General

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