COVID-19 has been spreading widely since January 2020, prompting the implementation of non-pharmaceutical interventions and vaccinations to prevent overwhelming the healthcare system. Our study models four waves of the epidemic in Munich over two years using a deterministic, biology-based mathematical model of SEIR type that incorporates both non-pharmaceutical interventions and vaccinations. We analyzed incidence and hospitalization data from Munich hospitals and used a two-step approach to fit the model parameters: first, we modeled incidence without hospitalization, and then we extended the model to include hospitalization compartments using the previous estimates as a starting point. For the first two waves, changes in key parameters, such as contact reduction and increasing vaccinations, were enough to represent the data. For wave three, the introduction of vaccination compartments was essential. In wave four, reducing contacts and increasing vaccinations were critical parameters for controlling infections. The importance of hospitalization data was highlighted, as it should have been included as a crucial parameter from the outset, along with incidence, to avoid miscommunication with the public. The emergence of milder variants like Omicron and a significant proportion of vaccinated people has made this fact even more evident.