A nested-epidemic model for the spread of hepatitis C among injecting drug users

Abstract

Injecting drug users (IDUs) are the largest risk group for HCV infection. Studying injecting by classical epidemiological methods is no easy task, largely due to its hidden nature and low prevalence in general population terms. Thus, mathematical modelling can be of major help in performing a qualitative and quantitative evaluation of the costs and possible impact of the various interventions and to produce forecasts of both injecting drug use and HCV spread among IDUs. In the present paper an epidemic Mover–Stayer model for the spread of drug use, which has been recently proposed, is extended to mirror the spread of an infectious disease, in particular hepatitis C, among the injecting drug user population. In order to model the spread of a disease (HCV) among a population evolving following a different epidemic (injecting drug use) all the compartments of the ‘external epidemic’ (injecting drug use) are subdivided into two sub-compartments: the first one comprising individuals who are not affected by HCV and the second one comprising individuals affected. The resulting model may be defined the ‘two epidemics’ or, better, the ‘nested epidemics’ model. The model is a Mover–Stayer model for what concerns the ‘external epidemic’ (injecting drug use) but is a homogeneous epidemic model for HCV (all individuals are at risk of HCV the same). In the following, the dynamic equations are derived. Some qualitative analysis is performed in order to evaluate the asymptotic behaviour and the impact of possible prevention or harm reduction interventions. The results of a scenario analysis are also presented. The model, though simple, seems to be a very valuable tool for policy makers.