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Introduction: Outbreaks of hepatitis C virus (HCV) infections among HIV-positive men who have sex with men (MSM) have been observed globally. Using a multi-modelling approach we estimate the time and number of direct-acting antiviral treatment courses required to achieve an 80% reduction in HCV prevalence among HIV-positive MSM in the state of Victoria, Australia., Methods: Three models of HCV transmission, testing and treatment among MSM were compared: a dynamic compartmental model; an agent-based model (ABM) parametrized to local surveillance and behavioural data ("ABM1"); and an ABM with a more heterogeneous population ("ABM2") to determine the influence of extreme variations in sexual risk behaviour., Results: Among approximately 5000 diagnosed HIV-positive MSM in Victoria, 10% are co-infected with HCV. ABM1 estimated that an 80% reduction in HCV prevalence could be achieved in 122 (inter-quartile range (IQR) 112 to 133) weeks with 523 (IQR 479 to 553) treatments if the average time from HCV diagnosis to treatment was six months. This was reduced to 77 (IQR 69 to 81) weeks if the average time between HCV diagnosis and treatment commencement was decreased to 16 weeks. Estimates were consistent across modelling approaches; however ABM2 produced fewer incident HCV cases, suggesting that treatment-as-prevention may be more effective in behaviourally heterogeneous populations., Conclusions: Major reductions in HCV prevalence can be achieved among HIV-positive MSM within two years through routine HCV monitoring and prompt treatment as a part of HIV care. Compartmental models constructed with limited behavioural data are likely to produce conservative estimates compared to models of the same setting with more complex parametrizations., (© 2018 The Authors. Journal of the International AIDS Society published by John Wiley & sons Ltd on behalf of the International AIDS Society.)