Mathematical Modeling and Optimal Control Strategy for a Discrete Time Drug Consumption Model

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of drug consumption. The population that we are going to study is divided into six compartments: potential drug users, light drug users, heavy drug users, heavy drug users-dealers and providers, temporary quitters of drug consumption, and permanent quitters of drug consumption. Our objective is to find the best strategy to reduce the number of light drug users, heavy drug users, heavy drug users-dealers and providers, and temporary quitters of drug consumption. We use four control strategies which are awareness programs through media and education, preventing contact through security campaigns, treatment, and psychological support along with follow-up. Pontryagin's maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the effectiveness of the optimization strategy.