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On Chaos of Discrete Time Fractional Order Host-Immune-Tumor Cells Interaction Model

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Abstract

In this study, we consider a three-dimensional discrete-time model to investigate the interaction between normal host cells with functional immune cells and tumor cells. Fixed point analysis is performed to study the stability of the discrete three-dimensional model and the sensitivity of the system analysis on the initial cell population. Necessary and sufficient conditions for optimal control of tumor cell growth have been created with the introduction of immune-chemotherapy drugs and the chaotic behavior of the system with branching having been demonstrated. The turbulence behavior of the system is shown by branching and Lyapunov power is performed for the integer-order discrete model and the turbulence effect is compared to the different fractional orders of the discrete model. Also, by numerical simulation, validating the theoretical results of the work and the effect of fractional derivative order on system chaos are investigated.

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Acknowledgements

The fourth author was supported by Miandoab Branch, Islamic Azad University. The fifth author was supported by Azarbaijan Shahid Madani University. The authors express their gratitude to dear unknown referees for their helpful suggestions which improved the final version of this paper.

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Authors and Affiliations

  1. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

    Jehad Alzabut

  2. Group of Mathematics, Faculty of Engineering, Ostim Technical University, 06374, Ankara, Turkey

    Jehad Alzabut

  3. Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Tamilnadu, 635601, India

    A. George Maria Selvam & Vignesh Dhakshinamoorthy

  4. Department of Mathematics, Miandoab Branch, Islamic Azad University, Miandoab, Iran

    Hakimeh Mohammadi

  5. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Shahram Rezapour

  6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Shahram Rezapour

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  1. Jehad Alzabut
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  2. A. George Maria Selvam
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Alzabut, J., Selvam, A.G.M., Dhakshinamoorthy, V. et al. On Chaos of Discrete Time Fractional Order Host-Immune-Tumor Cells Interaction Model. J. Appl. Math. Comput. 68, 4795–4820 (2022). https://doi.org/10.1007/s12190-022-01715-0

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