Are fast test results preferable to high test sensitivity in contact-tracing strategies?

Across the world, countries are fighting to reduce the spread of COVID-19. The backbone of the response is a test-trace-isolate strategy, where suspected infected get tested and isolated and possible secondary cases get traced, tested and isolated. Because more accurate tests often take longer to analyze, and the benefits of contact tracing are strengthened by rapid diagnosis, there exists a trade-off in test sensitivity and test waiting time in test-trace-isolate strategies. Here we ask: How many false negatives can be tolerated in a rapid test so that it reduces transmission better than a slower, more accurate test? How does this change with contact tracing efficiency and test waiting time? We find that a rapid, less sensitive test performs best for many test-parameter choices and that this is true even for modest contact tracing efficiency. For COVID-19-like viral parameters, a test with 40% false negatives and immediate result might reduce transmission as well as a test with no false negatives and a 3-day waiting time. Our analysis suggests employing rapid tests to reduce test waiting times as a viable strategy to reduce transmission when testing infrastructure is under stress.