Abstract
We present an optimal-control model for female drug abuse based on a nonlinear system of differential equations. The population is partitioned into susceptible (S), user (U), and recovered (R) classes. Two control variables are introduced: (prevention/education) and (treatment/rehabilitation). The objective functional
is minimized subject to the model dynamics. Using Pontryagin’s Maximum Principle, the necessary conditions for optimality are derived, and the forward–backward sweep method is employed for numerical simulations. Results show that combined early prevention and treatment rapidly reduce the user population and yield a lower cost functional than single interventions.
Keywords: Optimal Control, Female, Drug, Abuse, Nonlinear Differential Equation