Models for digitally contact-traced epidemics

TL;DR

This paper reviews mathematical models of digital contact tracing for COVID-19, introduces a new SEIR model with closed-form epidemic control conditions, and finds that high app uptake and rapid testing are essential for effectiveness.

Contribution

It proposes a novel SEIR model with analytical conditions for epidemic control based on contact tracing app penetration and testing efficiency.

Findings

High app uptake (>80%) and rapid testing (~1 day turnaround) are needed for digital contact tracing to control COVID-19.

Digital contact tracing alone is rarely sufficient to tame an epidemic without additional measures.

The model provides clear, analytical conditions to guide decision makers in epidemic control strategies.

Abstract

Contacts between people are the absolute drivers of contagious respiratory infections. For this reason, limiting and tracking contacts is a key strategy for the control of 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 the control of 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 proposed. In this article, we survey the main ones and we propose a 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 as a function of the contact tracing apps penetration and the 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. With our model, we find that digital contact tracing alone can rarely tame an 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.