A graph theoretical perspective of a drug abuse epidemic model

► We model substance abuse using a graph theoretical approach. ► The drug use epidemic is represented by a finite number of states and transition rules. ► Individuals are classified according to their drug use patterns with some drug users in treatment and others not. ► We examine the neighbourhood prevalence of each individual to determine some threshold values that determine whether drug use persists or dies out. ► Increasing the number of contacts has adverse effects as it results in increased numbers of drug users.