Using next generation matrices to estimate the proportion of infections that are not detected in an outbreak.

Contact tracing, where exposed individuals are followed up to break ongoing transmission chains, is a key pillar of outbreak response for infectious disease outbreaks. Unfortunately, these systems are not fully effective, and infections can still go undetected as people may not remember all their contacts or contacts may not be traced successfully. A large proportion of undetected infections suggests poor contact tracing and surveillance systems, which could be a potential area of improvement for a disease response. In this paper, we present a method for estimating the proportion of infections that are not detected during an outbreak. Our method uses next generation matrices that are parameterized by linked contact tracing data and case line-lists. We validate the method using simulated data from an individual-based model and then investigate two case studies: the proportion of undetected infections in the SARS-CoV-2 outbreak in New Zealand during 2020 and the Ebola epidemic in Guinea during 2014. We estimate that only 5.26% of SARS-CoV-2 infections were not detected in New Zealand during 2020 (95% credible interval: 0.243 - 16.0%) if 80% of contacts were under active surveillance but depending on assumptions about the ratio of contacts not under active surveillance versus contacts under active surveillance 39.0% or 37.7% of Ebola infections were not detected in Guinea (95% credible intervals: 1.69 - 87.0% or 1.70 - 80.9%).