Global dynamics and optimal control of a fractional-order HIV transmission model

Understanding HIV transmission dynamics aids effective prevention strategies. We construct a Caputo fractional-order HIV model with dual transmission modes and cytotoxic T lymphocyte (CTL) immune response. We prove solution well-posedness including existence, uniqueness, positivity and boundedness. We calculate the basic reproduction number R0 and analyze equilibrium stability: infection vanishes if R0<1, while HIV persists if R0>1. Sensitivity analysis proves transmission rates and immune strength dominate epidemic dynamics. Bifurcation analysis uncovers parameter-triggered nonlinear critical transitions. Optimal control is adopted to design transmission-cutting immune-boosting interventions. Numerical simulations using the FDE12 solver verify all theoretical findings. Compared with integer-order counterparts, fractional models better capture memory effects, providing guidance for HIV epidemic control.