To isolate, or not to isolate: a theoretical framework for disease control via contact tracing

Abstract

AbstractContact tracing is an essential tool in the public health battle for epidemiological control of infectious diseases. Contact tracing via case-by-case interviews is effective when contacts are known and outbreaks are small. Smartphone applications that keep track of contacts between users offer the possibility to scale contact tracing to larger outbreaks with minimal notification delays. While the benefits of reduced delays are widely recognised, it is less well understood how to best implement the tracing and notification protocol. The application will detect a multitude of contacts encountering an individual who later tests positive. Which of these contacts should be advised to self-isolate? The resolution hinges on an inherent trade-off: the more contacts notified, the greater the disease control, at the cost of more healthy individuals being instructed to self-isolate. In this study, based on a compartmental model tailored to the COVID-19 pandemic, we develop a framework to incorporate testing with limited resources coupled with a mechanistic description of digital contact tracing. Specifically, we employ a family of distributions characterising contact exposure and infection risk, and introduce a notification threshold that controls which level of exposure triggers notification. We detail how contact tracing can prevent disease outbreak, as a function of adoption rate, testing limitations, and other intervention methods such as social distancing and lockdown measures. We find an optimal notification threshold that balances the trade-off by minimising the number of healthy individuals instructed to self-isolate while preventing disease outbreak.