The hepatitis C virus (HCV) is a major health problem affecting an estimated 3% of the global population (World Health Organisation 2000). Just two decades after the virus was discovered, HCV is now the leading cause of liver disease in the world (Shepard et al. 2005). In Scotland, as well as other resource-rich countries, the majority of infections can be attributed to a history of injecting drug use. Around 50,000 people in Scotland are infected with HCV and the overwhelming majority of these infections are amongst current or former injecting drug users (ID Us) (Hutchinson, Roy et al., 2006). Services to prevent infections amongst IDUs, particularly HIV and HCV, have been around since the 1980s. Although these services appear to have been effective in preventing the transmission of HIV amongst IDUs in Scotland, they have been less effective in preventing the transmission of HCV in this population. Therefore, recent recommendations, such as those contained in the Hepatitis C Action Plan of the Scottish Government (Scottish Executive 2008b), have sought to improve intervention coverage within the IDU population and prevent the spread of HCV infection. Unfortunately, the dynamics of IDU populations and factors influencing the spread of HCV in this group are difficult to study. Mathematical modelling techniques are increasingly being used to understand the intricate relationship between the risk behaviour of IDUs and the transmission of HCV. In addition, these techniques are being used to understand the likely impact that different intervention strategies, treatment options, diagnostic tools and combinations of these have on the healthcare burden associated with HCV. Hence the work contained in this thesis will focus on the development and analysis of mathematical models which approximate the spread of HCV amongst IDUs. We will use these models to obtain HCV prevalence estimates for Glasgow ID Us and examine the effect that different parameter estimates and intervention measures have on our prevalence estimates. In particular, we are interested in finding situations which lead to the eventual elimination of HCV from the Glas- gow IDU population. For example, we wish to determine the number of needles and syringes that the Greater Glasgow and Clyde health board would need to distribute in order to eliminate HCV in this population. We now outline the work contained in this thesis before presenting the results of the literature search.