Fractal-fractional dynamics of HIV/AIDS: unveiling the synergistic impact of condoms, prophylaxis, and antiretroviral interventions for epidemic control
نویسندگان
1 Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, Nigeria
2 Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, Nigeria
3 Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
4 Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, Nigeria
5 Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, Nigeria
6 Department of Mathematics, SRM University Delhi-NCR, Sonepat-131029, Haryana, India
7 Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara, Punjab, India
8 Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, Nigeria
doi
10.22067/ijnao.2025.95479.1732چکیده
HIV/AIDS remains a global health crisis, with over 39 million people living with HIV in 2023, mainly in sub-Saharan Africa. This study presents a novel \textbf{fractal-fractional order model} to capture memory effects and heterogeneous transmission patterns in HIV dynamics. Unlike classical integer-order models, it integrates fractional derivatives (for long-term dependencies) and fractal dimensions (for self-similar contact networks). We prove solution positivity, boundedness, and compute the basic reproduction number $R_{0H}$, with global asymptotic stability at the endemic equilibrium when $R_{0H} > 1$. Sensitivity analysis identifies mortality, AIDS progression, contact rate, and treatment uptake as key $R_{0H}$ drivers. Fitted to South African data (2010--2023), the model estimates $R_{0H} \approx 0.95$ and projects a 28\% decline in new infections by 2033 under current trends. Numerical simulations using a second-order Adams-Bashforth scheme show lower fractional orders induce realistic oscillations, outperforming integer-order models in data fit and forecasting. Results underscore that \textbf{synergistic scale-up of condoms, PrEP, and ART} is critical to achieving HIV elimination.
