  Currently, many countries are considering the introduction of tracing
software on mobile smartphones with the main purpose to inform and alarm the
mobile app user. Here, we demonstrate that, in addition to alarming and
informing, mobile tracing can detect nearly all users that are infected by
SARS-CoV-2. Our algorithm BETIS (Bayesian Estimation for Tracing Infection
States) makes use of self-reports of the user's health status. Then, BETIS
guarantees that almost all SARS-CoV-2 infections of the group of users can be
detected. Furthermore, BETIS estimates the virus prevalence in the whole
population, consisting of users and non-users. BETIS is based on a hidden
Markov epidemic model and recursive Bayesian filtering. The potential that
mobile tracing apps, in addition to medical testing and quarantining, can
eradicate COVID-19 may persuade citizens to trade-off privacy against public
health.
