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Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells

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

Abstract

Mathematical models in epidemiology have been studied in the literature to understand the mechanism that underlies AIDS-related cancers, providing us with a better insight towards cancer immunity and viral oncogenesis. In this study, we propose a dynamical fractional order HIV-1 model in Caputo sense which involves the interactions between cancer cells, healthy CD4+T lymphocytes, and virus infected CD4+T lymphocytes leading to chaotic behavior. The model has been investigated for the existence and uniqueness of its solution via fixed point theory, while the unique non-negative solution remains bounded within the biologically feasible region. The stability analysis of the model is performed and the biological relevance of the equilibria is also discussed in the paper. The numerical simulations are obtained under different instances of fractional order α. It is observed that, as the fractional power decreases from ’one’ the chaotic behavior becomes more and more attractive. The existence of chaotic attractors for various species interaction has been observed in 2D and 3D cases. The time series evolution of the species showing different distributions under different fractional order α. The results show that order of the fractional derivative has a significant effect on the dynamic process.

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  • Naik, Parvaiz Ahmad & Owolabi, Kolade M. & Yavuz, Mehmet & Zu, Jian, 2020. "Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306688
    DOI: 10.1016/j.chaos.2020.110272
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    References listed on IDEAS

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    1. Owolabi, Kolade M., 2018. "Numerical patterns in reaction–diffusion system with the Caputo and Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 160-169.
    2. 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).
    3. 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).
    4. Naik, Parvaiz Ahmad & Zu, Jian & Ghoreishi, Mohammad, 2020. "Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. 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.
    6. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    7. 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:

    1. Mangal, Shiv & Misra, O.P. & Dhar, Joydip, 2023. "Fractional-order deterministic epidemic model for the spread and control of HIV/AIDS with special reference to Mexico and India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 82-102.
    2. Attaullah, & Jan, Rashid & Yüzbaşı, Şuayip, 2021. "Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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    4. Haoxiang Tang & Mingtao Li & Xiangyu Yan & Zuhong Lu & Zhongwei Jia, 2021. "Modeling the Dynamics of Drug Spreading in China," IJERPH, MDPI, vol. 18(1), pages 1-25, January.
    5. Özköse, Fatma & Yavuz, Mehmet & Şenel, M. Tamer & Habbireeh, Rafla, 2022. "Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. Atangana, Abdon & İğret Araz, Seda, 2021. "New concept in calculus: Piecewise differential and integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Doungmo Goufo, Emile F., 2022. "Linear and rotational fractal design for multiwing hyperchaotic systems with triangle and square shapes," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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