Fractal-fractional dynamics of HIV/AIDS: unveiling the synergistic impact of condoms, prophylaxis, and antiretroviral interventions for epidemic control

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 آبان 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.95479.1732

نویسندگان

Godwin Onuche Acheneje¹؛ Jeremiah Amos¹؛ Emmanuel Abah¹؛ William Atokolo¹؛ Agbata Benedict Celestine²؛ Kumawat Shyamsunder^{* 3}؛ A.K. Awasthi⁴؛ Bolarinwa Bolaji¹

¹Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, Nigeria

²Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria

³Department of Mathematics, SRM University Delhi-NCR, Sonepat-131029, Haryana, India

⁴Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara, Punjab, India

چکیده

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.

کلیدواژه‌ها

Fractal-fractional model؛ HIV/AIDS transmission dynamics؛ Basic reproduction number؛ Sensitivity analysis؛ Adams-Bashforth scheme