A three-state drug model of demand and supply : implications for a dynamic drug policy

Abstract

This thesis is devoted to the analysis of the so-called SAC model. It was introduced to identify the dependencies between active drug users, susceptibles, and drug supply in terms of a dynamic mathematical model. In previous theses, several analyses were carried out. Here, e.g., the behaviour of trajectories in the (S,A,C) space is studied in more detail, and the manifold separating the basins of attraction of two stable equilibria is shown from several angles to provide new insights.<br />The effects of supply shocks occuring close to an equilibrium are studied extensively.<br />Furthermore, an optimal control model with the control "enforcement" is formulated and equilibria of the canonical system are derived using Pontryagin's Maximum Principle.<br />Finally, the focus is on the price function of the SAC model, especially on its behaviour after a supply shock compared to the data for the Australian "heroin drought".