The emergence of COVID-19 favoured the development at Université de Montréal of an educational initiative aimed at promoting modelling and simulation in teaching and learning postsecondary mathematics. In our learning activities, modelling is not reduced to curve fitting; software is used and questions are asked to get a deeper understanding of the structure of a situation. In particular, compartmental epidemiological models were the topic of activities using digital tools (Insight Maker and Excel) that generated interest among teachers and students. With the possibilities offered by such tools of reflecting more adequately the complexity of the situation, we considered it relevant to model the perceptions related to significant effects of nonpharmaceutical interventions (NPIs) as well as the apparent social divide in behaviours regarding mandated measures and its effect on the epidemic. A study carried out on these aspects, based on data collected in Québec, led us to develop a new model which could form the basis for a new activity and be explored and further refined by students. This work leads to considering a social dimension to the teaching of modelling with differential equations and to include this teaching in the development of critical thinking.