A FRACTIONAL ORDER HIV/AIDS MODEL USING CAPUTO-FABRIZIO OPERATOR

Area of Science:

• Mathematical Biology
• Epidemiology
• Fractional Calculus

Background:

• Human Immunodeficiency Virus (HIV) targets the immune system, leading to Acquired Immunodeficiency Syndrome (AIDS) if untreated.
• HIV/AIDS poses a significant global health challenge, necessitating advanced modeling techniques for understanding disease dynamics.

Purpose of the Study:

• To develop and analyze a fractional order mathematical model for HIV/AIDS dynamics.
• To investigate the existence and uniqueness of solutions for the proposed HIV/AIDS model.
• To explore the application of the Caputo-Fabrizio operator in epidemiological modeling.

Main Methods:

• Employed fixed-point theory to establish the existence and uniqueness of solutions.
• Utilized the Caputo-Fabrizio fractional derivative operator, a non-conventional approach for biological models.
• Applied the iterative Laplace transform method to analyze model stability.

Main Results:

• The model exhibits two equilibrium points: disease-free and endemic.
• Conditions for the existence of the endemic equilibrium point were determined.
• The disease-free equilibrium point was proven to be locally asymptotically stable.
• The model's stability was confirmed through numerical simulations and the iterative Laplace transform method.

Conclusions:

• The fractional order HIV/AIDS model with the Caputo-Fabrizio operator offers enhanced precision and adaptability for patient data.
• Numerical simulations align with analytical results, highlighting the model's robustness.
• Fractional order derivatives provide advantages over classical approaches for analyzing HIV/AIDS dynamics, enabling better predictions.