Optimal control of a heroin epidemic mathematical model

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