Mathematical Modelling and Optimal Control Strategies in Drug Addiction Dynamics

Abstract

Drug abuse is a complex social and health problem that involves the individuals, their families, and societies at the international level. The tools that should be used in the understanding of its development should be based on the nonlinear and dynamic nature of addictive behavior. This is analyzed in terms of mathematical modeling. These models explain the changes in state, like susceptible, addicted, rehabilitated, and relapsed, depending on changes in the rate of contact, the efficacy of treatment, and the tendency to relapse. Through bifurcation behavior, stability analysis, and sensitivity studies, it is clear that a slight intervention or awareness change can cause dramatic changes in outcome. The basic reproduction number is another threshold measure that explains the continuation or the decline of addiction in a population. This review gives a summary of some of the key nonlinear modelling techniques, their assumptions, the way of analyzing them, and their use. It also indicates limitations, including a lack of real-time data and appropriate focus on psychological and social aspects. It is important to emphasize that synthesis presented the significance of additional data and more realistic models that can increase drug abuse prevention and rehabilitation and policy interventions.