We propose a novel epidemiological model, referred to as SEIHRDV, for the numerical simulation of the COVID-19 epidemic, validated using data from Italy starting in September 2020. SEIHRDV includes the following compartments: Susceptible (S), Exposed (E), Infectious (I), Healing (H), Recovered (R), Deceased (D), and Vaccinated (V). The model is age-stratified, with the population divided into 15 age groups, and it considers seven different contexts of exposure to infection (family, home, school, work, transport, leisure, and other contexts), which impact the transmission mechanism. The primary goal of this work is to provide a valuable tool for analyzing the spread of the epidemic in Italy during 2020 and 2021, supporting the country's decision making processes. By leveraging the SEIHRDV model, we analyzed epidemic trends, assessed the efficacy of non-pharmaceutical interventions, and evaluated vaccination strategies, including the introduction of the Green Pass, a containment measure implemented in Italy in 2021. The model proved instrumental in conducting comprehensive what-if studies and scenario analyses tailored to Italy and its regions. Furthermore, SEIHRDV facilitated accurate forecasting of the future potential trajectory of the epidemic, providing critical insights for improved public health strategies and informed decision making for authorities.