On the existence, uniqueness, stability, and numerical aspects for a novel mathematical model of HIV/AIDS transmission by a fractal fractional order derivative

• Published in: Journal of inequalities and applications 2024-03, Vol.2024 (1), p.36-21, Article 36
• Main Authors: Wu, Yanru, Nosrati Sahlan, Monireh, Afshari, Hojjat, Atapour, Maryam, Mohammadzadeh, Ardashir
• Format: Article
• Language: English
• Subjects: Acquired immune deficiency syndrome; AIDS; Analysis; Applications of Mathematics; Collocation methods; Coronaviruses; COVID-19; Disease prevention; Disease transmission; Epidemics; Fractal fractional derivative; Fractal models; Fractals; Fractional calculus; Gegenbauer polynomials; Health care; HIV; Human immunodeficiency virus; Immune system; Infections; Investigations; Mathematical analysis; Mathematical model of HIV/AIDS transmission; Mathematical models; Mathematics; Mathematics and Statistics; Polynomials; Stability; Stability analysis; Uniqueness; α-ψ-Geraghty type contraction
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-024-03098-1

In this study, we explore a mathematical model of the transmission of HIV/AIDS. The model incorporates a fractal fractional order derivative with a power-law type kernel. We prove the existence and uniqueness of a solution for the model and establish the stability conditions by employing Banach’s contraction principle and a generalized α - ψ -Geraghty type contraction. We perform stability analysis based on the Ulam–Hyers concept. To calculate the approximate solution, we utilize Gegenbauer polynomials via the spectral collocation method. The presented model includes two fractal and fractional order derivatives. The influence of the fractional and fractal derivatives on the outbreak of HIV is investigated by utilizing real data from the Cape Verde Islands in 1987–2014.