Models for Digitally Contact-Traced Epidemics

Contacts between people are the main drivers of contagious respiratory infections. For this reason, limiting and tracking contacts is a key strategy for controlling the COVID-19 epidemic. Digital contact tracing has been proposed as an automated solution to scale up traditional contact tracing. However, the required penetration of contact tracing apps within a population to achieve a desired target in controlling the epidemic is currently under discussion within the research community. In order to understand the effects of digital contact tracing, several mathematical models have been studied. In this article, we propose a novel compartmental SEIR model with which it is possible, differently from the models in the related literature, to derive closed-form conditions regarding the control of the epidemic. These conditions are a function of the penetration of contact tracing applications and testing efficiency. Closed-form conditions are crucial for the understandability of models, and thus for decision makers (including digital contact tracing designers) to correctly assess the dependencies within the epidemic. Feeding COVID-19 data to our model, we find that digital contact tracing alone can rarely tame the epidemic: for unrestrained COVID-19, this would require a testing turnaround of around 1 day and app uptake above 80% of the population, which are very difficult to achieve in practice. However, digital contact tracing can still be effective if complemented with other mitigation strategies, such as social distancing and mask-wearing.