(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
The HIV/AIDS epidemic profoundly affects the working-class population, resulting in increased mortality and morbidity rates and causing substantial labour loss across various sectors. To assess the epidemic’s impact on the specified class, a fractal-fractional-order mathematical model was formulated based on Atangana-Baleanu-Caputo operator. This model encompasses seven compartments, and the existence and uniqueness of its solutions were verified based on the Banach fixed-point theorem, contraction mapping concepts, and Hyers-Ulam stability criteria. The mathematical model was analyzed to understand the effects of HIV/AIDS on the working-class population. Real data from Ethiopia were utilized to validate the model. Subsequently, the model was extended to optimal control fractal-fractional models, incorporating different control strategies. Numerical simulations were performed using MATLAB R2019a to support the analytical solutions. The study’s results demonstrated that the fractal-fractional-order model provides a comprehensive understanding of the complexities of HIV/AIDS infection. The findings suggested that increasing the number of infected productive members of the population can help to control the spread of the disease by reducing the inequality caused by HIV/AIDS. Furthermore, the numerical simulation of the optimal control model indicated that decreasing non-productivity reduces the number of infected individuals. Therefore, effective management of the infection holds the potential to eradicate the disease in the country.