New model of HIV-AIDS dynamics based on the Caputo–Fabrizio derivative: Optimal strategies for controlling the spread

Nassira Madani; Zakia Hammouch; EL Houssine Azroul

doi:10.1016/j.jocs.2025.102612

New model of HIV-AIDS dynamics based on the Caputo–Fabrizio derivative: Optimal strategies for controlling the spread

Nassira Madani, Zakia Hammouch^*, EL Houssine Azroul

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The goal of this study is to introduce a new model to better understand the spread of HIV/AIDS, with a particular focus on individuals who are unaware of their infection status. We propose and analyze a new Caputo–Fabrizio fractional model, examining its local stability around the equilibrium point using the abdicate method tailored for Caputo–Fabrizio derivatives. To assess global stability, we employ linear matrix inequalities (LMI). Furthermore, we formulate a fractional optimal control problem to identify effective strategies for controlling the disease. Numerical simulations are conducted to confirm the stability of the equilibrium and to demonstrate the behavior of the proposed solutions.

Original language	English
Article number	102612
Journal	Journal of Computational Science
Volume	90
DOIs	https://doi.org/10.1016/j.jocs.2025.102612
Publication status	Published - Aug 2025
Externally published	Yes

Keywords

Basic reproduction number
Caputo–Fabrizio derivative
HIV/AIDS
Sensitivity analysis
Stability analysis

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.jocs.2025.102612

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title = "New model of HIV-AIDS dynamics based on the Caputo–Fabrizio derivative: Optimal strategies for controlling the spread",

abstract = "The goal of this study is to introduce a new model to better understand the spread of HIV/AIDS, with a particular focus on individuals who are unaware of their infection status. We propose and analyze a new Caputo–Fabrizio fractional model, examining its local stability around the equilibrium point using the abdicate method tailored for Caputo–Fabrizio derivatives. To assess global stability, we employ linear matrix inequalities (LMI). Furthermore, we formulate a fractional optimal control problem to identify effective strategies for controlling the disease. Numerical simulations are conducted to confirm the stability of the equilibrium and to demonstrate the behavior of the proposed solutions.",

keywords = "Basic reproduction number, Caputo–Fabrizio derivative, HIV/AIDS, Sensitivity analysis, Stability analysis",

author = "Nassira Madani and Zakia Hammouch and Azroul, \{EL Houssine\}",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier B.V.",

year = "2025",

month = aug,

doi = "10.1016/j.jocs.2025.102612",

language = "English",

volume = "90",

journal = "Journal of Computational Science",

issn = "1877-7503",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - New model of HIV-AIDS dynamics based on the Caputo–Fabrizio derivative

T2 - Optimal strategies for controlling the spread

AU - Madani, Nassira

AU - Hammouch, Zakia

AU - Azroul, EL Houssine

PY - 2025/8

Y1 - 2025/8

N2 - The goal of this study is to introduce a new model to better understand the spread of HIV/AIDS, with a particular focus on individuals who are unaware of their infection status. We propose and analyze a new Caputo–Fabrizio fractional model, examining its local stability around the equilibrium point using the abdicate method tailored for Caputo–Fabrizio derivatives. To assess global stability, we employ linear matrix inequalities (LMI). Furthermore, we formulate a fractional optimal control problem to identify effective strategies for controlling the disease. Numerical simulations are conducted to confirm the stability of the equilibrium and to demonstrate the behavior of the proposed solutions.

AB - The goal of this study is to introduce a new model to better understand the spread of HIV/AIDS, with a particular focus on individuals who are unaware of their infection status. We propose and analyze a new Caputo–Fabrizio fractional model, examining its local stability around the equilibrium point using the abdicate method tailored for Caputo–Fabrizio derivatives. To assess global stability, we employ linear matrix inequalities (LMI). Furthermore, we formulate a fractional optimal control problem to identify effective strategies for controlling the disease. Numerical simulations are conducted to confirm the stability of the equilibrium and to demonstrate the behavior of the proposed solutions.

KW - Basic reproduction number

KW - Caputo–Fabrizio derivative

KW - HIV/AIDS

KW - Sensitivity analysis

KW - Stability analysis

UR - https://www.scopus.com/pages/publications/105007598835

U2 - 10.1016/j.jocs.2025.102612

DO - 10.1016/j.jocs.2025.102612

M3 - Article

AN - SCOPUS:105007598835

SN - 1877-7503

VL - 90

JO - Journal of Computational Science

JF - Journal of Computational Science

M1 - 102612

ER -

New model of HIV-AIDS dynamics based on the Caputo–Fabrizio derivative: Optimal strategies for controlling the spread

Abstract

Keywords

UN SDGs

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