An Age-Structured Single-State Drug Initiation Model: Cycles of Drug Epidemics and Optimal Prevention Programs

This paper introduces a model for drug initiation that extends traditional dynamic models by considering explicitly the age distribution of the users. On the basis of a 2-groups model in which the population is split up in an user and a non-user group the advantage of a continuous age distribution is shown by considering more details and by yielding new results. Neglecting death rates allows to reduce the model to a single state (1-group) descriptive model which is capable to simulate the complex behavior of drug epidemics. Furthermore, prevention programs – especially school-based programs – can be targeted to certain age classes. So in order to discover how best to allocate resources to prevention programs over different age classes we formulate and solve also optimal control models.