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

Majda El Younoussi, Zakaria Hajhouji, Khalid Hattaf and Noura Yousfi
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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
Noura Yousfi: Hassan II University of Casablanca, Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M’Sick

A chapter in Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics, 2023, pp 125-136 from Springer

Abstract: 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.

Keywords: Virotherapy; M1 virus; Hattaf time-fractional derivative; Reaction-diffusion; Stability (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-33050-6_7

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DOI: 10.1007/978-3-031-33050-6_7

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