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The discovery of highly effective hepatitis C virus (HCV) treatments has led to discussion of elimination and intensified interest in models of HCV transmission. In developed settings, HCV disproportionally affects people who inject drugs (PWID), with models typically used to provide an evidence base for the effectiveness of interventions such as needle and syringe programs, opioid substitution therapy and more recently treating PWID with new generation therapies to achieve specified reductions in prevalence and / or incidence. This manuscript reviews deterministic compartmental S-I, deterministic compartmental S-I-S and network-based transmission models of HCV among PWID. We detail typical assumptions made when modelling injecting risk behaviour, virus transmission, treatment and re-infection and how they correspond with available evidence and empirical data.
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