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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.

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

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  • 发表日期：

    2025年

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  • Zakaria Hajhouji,
  • Hamza El Mamouni,
  • Khalid Hattaf,
  • Noura Yousfi

摘要

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.