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.
The ongoing COVID-19 pandemics disproportionately affects people from Black and African American backgrounds. We propose a model to quantify the dynamic segregation of ethnicities in a city, based on passage times and coverage times of random walks on graphs. The results confirm that knowing where people commute to, rather than where they live, is potentially much more important to contain and curb the spreading of infectious diseases.