Early evidence during the first phase of the COVID-19 outbreak shows that individuals facing the risk of infection increased their levels of physical distancing even before relevant measures were imposed. Not taking individual behaviour into account can lead policy makers to overestimate the infection risks in absence of physical distancing measures and underestimate the effectiveness of measures. This paper proposes a behavioural-compartmental-epidemiological model with heterogenous agents who take physical distancing measures to reduce the risk of becoming infected. The level of these measures depends on the government’s regulations and the daily new cases and is influenced by the individual perception of the infection risk. This approach can account for two important factors: (i) the limited information about the exact infection risks and (ii) the heterogeneity across individuals with regards to physical distancing decisions. We find that the intensity of measures required to reduce infections is directly related to the public perception of the risk of infection, and that harsher late measures are in general less effective than milder ones imposed earlier. The model demonstrates that the feedback effects between contagion dynamics and individual decisions make the extrapolation of out-of-sample forecasts from past data dangerous, in particular in a context with high uncertainty.