AbstractsMathematics

By sharing injecting equipment, blood borne infections are spread among Injecting Drug Users (IDU). One infection that affects many IDU is the Hepatitis C Virus (HCV), which can cause liver cirrhosis and liver carcinoma. The virus that causes AIDS, HIV, is also spread by this route. In this thesis, the simultaneous spread of HCV and HIV among IDU is addressed using mathematical modelling. Policy aimed at reducing the damage that drug users cause to themselves and to society is denoted by Harm Reduction. This includes educating drug users and providing them with clean injection equipment or substitution therapy. Recently, much attention is given to the concept of treatment as prevention. HIV medication strongly lowers infectiousness of an individual, and HCV may be cured, also stopping any further transmission. We addressed the impact of such measures. We used several quite different types of models, which were useful for studying different types of questions. We first developed a deterministic model of the spread of both HIV and HCV among IDU. This showed how the eventual HIV to HCV prevalence ratio is determined by the distribution of risk-behaviour within a population. In order to evaluate the effects of Harm Reduction policy in Amsterdam, we created a highly detailed model, describing the spread of HIV and HCV among IDU in this town within the past fifty years. For this individual-based model, parameters were informed by the Amsterdam Cohort Studies among IDU. We could not show large policy effects; although syringe sharing may have been lowered substantially, much of the noted decline in viral spread could be explained by ageing of the population and the natural progression of the epidemics. Next, we adapted this individual based model to analyse the impact that starting HIV-treatment in an earlier stage of infection could have. Such policy may strongly impact the number of HIV cases, if implemented within the first few years of an HIV outbreak. Treatment effects were overestimated when we assumed that all IDU share syringes equally often. To study per individual benefits of intervention or treatment, we used probability calculation. This included the likelihood of preventing infection for the individual under intervention, as well as the expected number of prevented infections to other IDU. Targeting interventions by syringe sharing risk-behaviour of IDU could make policy much more effective, but who are best targeted may depend on the infection and circumstances under consideration. For example, who are best treated first for HCV was found to be determined by the HCV prevalence; only at higher prevalence are lowest-risk-behaviour IDU best treated. Syringe sharing risk-behaviour is likely to be highly variable among IDU, and this heterogeneity will impact on the effects of policy aimed at lowering the spread of infections. To properly judge the impact of past policy this heterogeneity, as well as demographic changes over time, should not be ignored. Worryingly, ignoring risk…