Increasing access to direct-acting antiviral (DAA) treatment for hepatitis C virus (HCV) infection and decelerating the rise in high-risk behaviour over the next decade could curb the HCV epidemic among HIV-positive men who have sex with men (MSM). We investigated if similar outcomes would be achieved by short-term intensive interventions like the Swiss-HCVree-trial. We used a HCV transmission model emulating two 12-months intensive interventions combining risk counselling with (i) universal DAA treatment (pangenotypic intervention) and (ii) DAA treatment for HCV genotypes 1 and 4 (replicating the Swiss-HCVree-trial). To capture potential changes outside intensive interventions, we varied time from HCV infection to treatment in clinical routine and overall high-risk behaviour among HIV-positive MSM. Simulated prevalence dropped from 5.5% in 2016 to ≤2.0% over the intervention period (June/2016-May/2017) with the pangenotypic intervention, and to ≤3.6% with the Swiss-HCVree-trial. Assuming time to treatment in clinical routine reflected reimbursement restrictions (METAVIR ≥F2, 16.9 years) and stable high-risk behaviour in the overall MSM population, prevalence in 2025 reached 13.1% without intensive intervention, 11.1% with the pangenotypic intervention and 11.8% with the Swiss-HCVree-trial. If time to treatment in clinical routine was 2 years, prevalence in 2025 declined to 4.8% without intensive intervention, to 2.8% with the pangenotypic intervention, and to 3.5% with the Swiss-HCVree-trial. In this scenario, the pangenotypic intervention and the Swiss-HCVree-trial reduced cumulative (2016-2025) treatment episodes by 36% and 24%, respectively. Therefore, intensive interventions could reduce future HCV treatment costs and boost the benefits of long-term efforts to prevent high-risk behaviour and to reduce treatment delay. But if after intensive interventions treatment is deferred until F2, short-term benefits of intensive interventions would dissipate in the long term.