Optimal control strategies for mitigating drug addiction: A mathematical modeling approach

Drug addiction is widely recognized as a complex social issue influenced by various socio-economic and environmental factors. This study addresses the dynamics of drug addiction through a mathematical modeling approach, integrating epidemiological insights with optimal control strategies. Our model employs two control strategies, prevention and punishment, to reduce drug addiction using the Pontryagin Maximum Principle for optimal control. The model emphasizes the roles of “preventive measures” and “punishment strategies” controls in mitigating drug addiction within a community context. Numerical simulations conducted using MATLAB explore the potential impact of these controls on the transmission dynamics of drug addiction, offering insights into how they could reduce the addicted population and promote recovery. The findings highlight the importance of integrated interventions that combine social, psychological, and medical approaches to combat drug addiction effectively.