A heroin epidemic mathematical model with prevention information and
treatment, as control interventions, is analyzed, assuming that an individual's
behavioral response depends on the spreading of information about the effects
of heroin. Such information creates awareness, which helps individuals to
participate in preventive education and self-protective schemes with additional
efforts. We prove that the basic reproduction number is the threshold of local
stability of a drug-free and endemic equilibrium. Then, we formulate an optimal
control problem to minimize the total number of drug users and the cost
associated with prevention education measures and treatment. We prove existence
of an optimal control and derive its characterization through Pontryagin's
maximum principle. The resulting optimality system is solved numerically. We
observe that among all possible strategies, the most effective and cost-less is
to implement both control policies.publishe
