Fractional-order modeling of HIV/AIDS dynamics in the working-class population using the ABC operator

HIV/AIDS remains a major global health problem that is strongly shaped by socioeconomic conditions and workforce productivity. This work develops and analyses a deterministic HIV/AIDS model for a working-class population, distinguishing productive and non-productive susceptible and infected groups, and extends it to an Atangana-Baleanu-Caputo (ABC) fractional-order framework. The integer-order system is analysed in terms of positivity, boundedness, equilibrium points, the basic reproduction number, local and global stability, and backward bifurcation using the Castillo-Chavez and Song center-manifold approach. The fractional-order model is shown to be mathematically well posed by using fixed-point arguments, Lipschitz conditions and Hyers-Ulam stability, and is approximated numerically with the Toufik-Atangana scheme. An optimal control problem with prevention and productivity-enhancing interventions is formulated and solved, and cost-effectiveness of alternative strategies is assessed. Numerical simulations indicate that combining prevention with measures that reduce non-productivity substantially lowers HIV burden and improves workforce productivity, while the fractional model better reflects gradual temporal dynamics compared with the classical system.