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A Reaction-Diffusion Fractional Model for Cancer Virotherapy with Immune Response and Hattaf Time-Fractional Derivative

In: Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics

Author

Listed:
  • Majda El Younoussi

    (Hassan II University of Casablanca, Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick)

  • Zakaria Hajhouji

    (Hassan II University of Casablanca, Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick)

  • Khalid Hattaf

    (Hassan II University of Casablanca, Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick
    Centre Régional des Métiers de l’Education et de la Formation (CRMEF), Equipe de Recherche en Modélisation et Enseignement des Mathématiques (ERMEM))

  • Noura Yousfi

    (Hassan II University of Casablanca, Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick)

Abstract

Recently, fractional partial differential equations (FPDEs) play a crucial role in the modeling of the dynamics of many systems arising from biology and other fields of science and engineering. The aim of this work is to model the interaction between nutrient, normal cells, tumor cells, M1 virus, and cytotoxic T lymphocyte (CTL) cells by using the new generalized Hattaf fractional (GHF) derivative. The mathematical model describing such type of interaction is rigorously formulated. Furthermore, the dynamical behaviors of the model are determined by three threshold parameters, namely, the ability of absorbing nutrient by normal cells, the ability of absorbing nutrient by tumor cells, and the reproduction number for cellular immunity.

Suggested Citation

  • Majda El Younoussi & Zakaria Hajhouji & Khalid Hattaf & Noura Yousfi, 2023. "A Reaction-Diffusion Fractional Model for Cancer Virotherapy with Immune Response and Hattaf Time-Fractional Derivative," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics, pages 125-136, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-33050-6_7
    DOI: 10.1007/978-3-031-33050-6_7
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    JEL classification:

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

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