Abstract Drug use and problems change dramatically over time in ways that are often described as reflecting an “epidemic cycle”. We use simulation of a model of drug epidemics to investigate how the relative effectiveness of different types of prevention varies over the course of such an epidemic. Specifically we use the so-called LHY model (see, Discussion Paper No. 251 of the Institute of Econometrics, OR, and Systems Theory, Vienna University of Technology, Vienna, Austria, 2000) which includes both “contagious” spread of initiation (a positive feedback) and memory of past use (a negative feedback), which dampens initiation and, hence, future use. The analysis confirms the common sense intuition that prevention is more highly leveraged early in an epidemic, although the extent to which this is true in this model is striking, particularly for campaigns designed to preserve or amplify awareness of the drug's dangers. The findings also suggest that the design of “secondary” prevention programs should change over the course of an epidemic.