The relevance of the investigation is due to the need to optimize the system for the primary prevention of drug addiction and use because of its insufficient efficiency in the Russian Federation. This problem is manifested in the low awareness of the population, primarily young people, about the negative consequences of the use of narcotic drugs and psychotropic substances and about the high associated risk of their involvement in the use of narcotics, including new types of psychotropic substances (synthetic narcotics). In this connection, the aim of our investigation was to develop a method for determining the potential efficiency of measures for the primary prevention of drug addiction and use, by applying mathematical modeling. The Kermak—McKendrick epidemic model of the susceptible infected removed (SIR) — like type was used as a basis to build a drug use spread model that represented as transition of groups of individuals from one state to another in relation to drug use. This gave rise to a simulation model estimating the magnitude of a drug use reduction in the risk group in relation to the initial one if varying effective preventive measures were implemented. The drug abuse scenario in case of effective measures was analyzed. Enhancing the effectiveness of measures for primary prevention of drug addiction was shown to lead to a stronger rather than linear decline in the size of a group at risk for drug and in the number of drug users. This model may be used to prepare programs, strategies for the primary prevention of drug addiction to evaluate their potential effectiveness.