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Dynamics of a reaction-diffusion fractional-order model for M1 oncolytic virotherapy with CTL immune response

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  • Younoussi, Majda El
  • Hajhouji, Zakaria
  • Hattaf, Khalid
  • Yousfi, Noura

Abstract

Despite many years of research, cancer continues to be a major worldwide concern. Several researchers proposed their mathematical models to understand and describe the dynamics of tumor cells under some cancer treatments. In this paper, we present a fractional partial differential equation system to describe the dynamics in space and time of the concentration of normal cells, tumor cells, nutrient, M1 virus, and cytotoxic T lymphocytes (CTL) cells, as well as the interaction between them. We study and analyze the equilibrium points of the presented system. The global stability of these equilibrium points is proved by constructing adequate Lyapunov functional for each equilibrium point. Furthermore, we give some numerical simulations to illustrate our results.

Suggested Citation

  • Younoussi, Majda El & Hajhouji, Zakaria & Hattaf, Khalid & Yousfi, Noura, 2022. "Dynamics of a reaction-diffusion fractional-order model for M1 oncolytic virotherapy with CTL immune response," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001679
    DOI: 10.1016/j.chaos.2022.111957
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    References listed on IDEAS

    as
    1. Khalid Hattaf, 2021. "Stability of Fractional Differential Equations with New Generalized Hattaf Fractional Derivative," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-7, December.
    2. Elaiw, A.M. & Hobiny, A.D. & Al Agha, A.D., 2020. "Global dynamics of reaction-diffusion oncolytic M1 virotherapy with immune response," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    3. Khalid Hattaf & Noura Yousfi, 2020. "Global Stability for Fractional Diffusion Equations in Biological Systems," Complexity, Hindawi, vol. 2020, pages 1-6, August.
    4. Majda El Younoussi & Zakaria Hajhouji & Khalid Hattaf & Noura Yousfi & Constantin Udriste, 2021. "A New Fractional Model for Cancer Therapy with M1 Oncolytic Virus," Complexity, Hindawi, vol. 2021, pages 1-12, June.
    5. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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    Cited by:

    1. Stamova, Ivanka & Stamov, Trayan & Stamov, Gani, 2022. "Lipschitz stability analysis of fractional-order impulsive delayed reaction-diffusion neural network models," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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    More about this item

    Keywords

    Oncolytic virotherapy; Fractional-derivative; Immune response; Reaction-diffusion; M1 virus;
    All these keywords.

    JEL classification:

    • M1 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration

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