The Fractal-Fractional Mathematical Model Analysis of the Impact of HIV/AIDS on the Working-Class in Ethiopia (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 onthe specified class, a fractal-fractional-order mathematical model was formulated based on Atangana-Baleanu-Caputo operator. This model encompassesseven compartments, and the existence and uniqueness of its solutions wereverified 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, themodel was extended to optimal control fractal-fractional models, incorporating different control strategies. Numerical simulations were performed usingMATLAB R2019a to support the analytical solutions. The study’s resultsdemonstrated that the fractal-fractional-order model provides a comprehensive understanding of the complexities of HIV/AIDS infection. The findingssuggested that increasing the number of infected productive members of thepopulation can help to control the spread of the disease by reducing the inequality caused by HIV/AIDS. Furthermore, the numerical simulation of theoptimal control model indicated that decreasing non-productivity reduces thenumber of infected individuals. Therefore, effective management of the infection holds the potential to eradicate the disease in the country.
Keywords: Hyers-Ulam stability; HIV/AIDS; working-class population; optimal-control; fractional order; fractal-fractional.