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Spatiotemporal Dynamics of a Mathematical HIV-1 Infection Model with Hattaf Time Fractional Derivative and Two Types of Infected Cells

In: Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells

Author

Listed:
  • Zakaria Hajhouji

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

  • Hamza El Mamouni

    (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

In this paper, we propose and analyze the spatiotemporal dynamics of a fractional model for human immunodeficiency virus 1 (HIV-1) formulated by partial differential equations of reaction-diffusion type. The reaction is modeled by the Hattaf time-fractional derivative and the diffusion is described by the Laplacian operator. The proposed model incorporates two types of treatment, humoral immunity and highly active antiretroviral therapy (HAART), in order to reduce the viral load in patients infected with HIV-1 and prevent the development of HIV-related complications.

Suggested Citation

  • Zakaria Hajhouji & Hamza El Mamouni & Khalid Hattaf & Noura Yousfi, 2025. "Spatiotemporal Dynamics of a Mathematical HIV-1 Infection Model with Hattaf Time Fractional Derivative and Two Types of Infected Cells," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells, pages 307-321, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-97461-8_17
    DOI: 10.1007/978-3-031-97461-8_17
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