The initial rollout of COVID-19 vaccines has been challenged by logistical issues, limited availability of doses, scarce healthcare capacity, spotty acceptance, and variants of concern. Non-pharmaceutical interventions (NPIs) have been critical to support these phases. At the same time, the arrival of vaccines might have changed the risk assessment of some leading to a behavioural relaxation of NPIs. Several epidemic models have investigated the potential effects of this phenomenon on the COVID-19 pandemic, but they have not been validated against data. Recent empirical evidence, obtained via surveys, provides conflicting results on the matter. Hence, the extent behavioural relaxation induced by COVID-19 vaccines is still far from clear. Here, we aim to study this phenomenon in four regions. To this end, we implement five realistic epidemic models which include age structure, multiple virus strains, NPIs, and vaccinations. One of the models acts as a baseline, while the other four extend it and, building on the literature, include different behavioural relaxation mechanisms. First, we set the stage by calibrating the baseline model and running counterfactual scenarios to quantify the impact of vaccinations and NPIs. Our results confirm the critical role of both in reducing infection and mortality rates. Second, we calibrate the four behavioural models to real data and compare them to each other and to the baseline. While behavioural models offer a better fit of weekly deaths in all regions, this improvement is offset by their increased complexity in three locations. In the region where one of the behavioural model emerges as the most likely, our findings suggest that relaxation of NPIs led to a relative increase of deaths of more than $8\%$, highlighting the potential negative effect of this phenomenon. Overall, our work contributes to the retrospective validation of epidemic models developed amid the COVID-19 Pandemic.
