We tackle the problem of quantifying the effectiveness of digital contact-tracing (CT) in containing the spreading of a non-airborne disease, like SARS-COV-2. We moved from the observation that the adoption rate of digital contact tracing apps during the COVID-19 pandemic has been generally pretty low (between 5\% and 20\% of the population in Western countries), and that the strategy" used by governments to encourage people to install contact-tracing apps effectively corresponds to selecting those individuals uniformly at random.