A novel compartmental model that includes vaccination strategy, permanence in hospital wards and tracing of infected individuals has been implemented to forecast hospital overload caused by COVID-19 pandemics in Italy. The model parameters were calibrated according to available data on cases, hospital admissions, and number of deaths in Italy during the second wave, and were validated in the timeframe corresponding to the first successive wave where vaccination campaign was fully operational. This model allowed quantifying the decrease of hospital demand in Italy associated with the vaccination campaign. Clinical relevance This study provides evidence for the ability of deterministic SIR-based models to accurately forecast hospital demand dynamics, and support informed decisions regarding dimensioning of hospital personnel and technologies to respond to large-scale epidemics, even when vaccination campaigns are available.