Modeling and mathematical analysis of drug addiction with the study of the effect of psychological and biological treatment

In this article, we propose a discrete mathematical model which describes the propagation of drug phenomenon in human population. The population is unscrewed five compartments: "S" People likely to become addicts, "M" Moderate "H" Heavy "T" receiving addiction treatment, "R" recovered people who have completely abstained from addiction. Our goal find better strategy reduce number heavy addicts and maximize full treatment. tools optimal control theory were used study, particular Pontryagin maximum principle.