In the fight against the COVID-19 pandemic, lockdowns have succeeded in limiting contagions in many countries, at however heavy societal costs: more targeted non-pharmaceutical interventions are desirable to contain or mitigate resurgences. Contact tracing, by identifying and quarantining people who have been in prolonged contact with an infectious individual, has the potential to stop the spread where and when it occurs, with thus limited impact. The limitations of manual contact tracing (MCT), due to delays and imperfect recall of contacts, might be compensated by digital contact tracing (DCT) based on smartphone apps, whose impact however depends on the app adoption. To assess the efficiency of such interventions in realistic settings, we use datasets describing contacts between individuals in several contexts, namely a university campus, offices, and a highschool, with high spatial and temporal resolution, to feed numerical simulations of a realistic compartmental model for COVID-19. This model includes contagious presymptomatics and a distinction between asymptomatics and symptomatics with mild or severe symptoms. We implement standard measures of detection and isolation of severe cases, with a tunable probability of detection of mild cases, and simulate in addition MCT and DCT, taking into account their respective limitations (limited app adoption, limited efficiency and delays of MCT, limited compliance) and considering various thresholds to define at-risk contacts. We find that the obtained reduction of epidemic size has a robust behavior as a function of the MCT and DCT efficiencies, independently of datasets and parameters: this benefit is linear in the fraction of contacts recalled during MCT, and quadratic in the app adoption, with no threshold effect. The combination of tracing strategies can yield important benefits, and the cost (number of quarantines) vs. benefit curve has a typical parabolic shape, independent on the type of tracing, with a high benefit and low cost if app adoption and MCT efficiency are high enough. Our numerical results are qualitatively confirmed by analytical results on simplified models.
