Operational models for epidemic of problematic drug use: the Mover-Stayer approach to heterogeneity

A modified version of a susceptibles–infectives–removed (S–I–R) model for the HIV/AIDS epidemic, proposed at the beginning of the 1990s and recently generalized, is presented to mirror the epidemics of problematic drug use. The generalized model, which belongs to the susceptibles–infectives–susceptibles (S–I–S) class of epidemic models, can be used both to estimate interesting epidemic macro-parameters and to make scenario analyses. The model is a compartmental Mover–Stayer-type structure (Soc. Methods Res. 11 (1983) 345; Bull. Narcotics LIII (1-2) (2001) 39; Biometrics 55(4) (1999) 1252; Math. Biosci. 107 (1991) 521) and allows taking into account possible heterogeneous behaviours of the susceptibles. Such models, in fact, consider the susceptible population as subdivided into two main groups: the group of stayers, that is, the group of individuals who are considered not at risk of ‘‘infection’’, and the group of movers (possibly divided into sub-groups with different risk behaviour) who are at risk of infection. Due to the interactions between infectious individuals and the susceptibles, some of these may pass to the drug user compartments and begin a ‘‘drug user career’’. The model is presented and studied from a qualitative point of view using a Markov hybrid approximation. Some qualitative evaluation of the possible impact of interventions directed both towards susceptibles (primary prevention) and towards users (secondary prevention and/or law enforcement) are presented. Specific ‘‘what if’’ scenario analyses are obtained by simulation. Possible future developments are outlined.