Drug user dynamics: A compartmental model of drug users for scenario analyses

Abstract

A six-typology compartment model of trends in the use of illicit drugs in Italy is developed to evaluate policies and interventions through scenario analyses. Inside the big compartments of just-cannabis users and multiple drug users, three subpopulations are taken into account: the occasional, regular and intensive user. Moreover, compartments for health care, assisted persons together with a constant source (susceptible) are added; removed people (i.e. those who leave drugs for any reason) are put in a compartment which does not participate in the dynamics. Flows from the susceptible reservoir among the drug-user compartments and to the removed or the health care compartments are studied in a deterministic linear ODE framework, where parameters are estimated using Italian data. This system shows an evolution towards a steady state, the speed of convergence being dependent on parameters in a fairly visible way. This model represents a theoretical development in drug policy analysis, as it shows the relevance of flux parameters, which are in principle subject to modifications due to institutional efforts, together with a quantitative evaluation of their role in the evolution of the whole system.