RESPECT the UNSTABLE: DELAYS and SATURATION in CONTACT TRACING for DISEASE CONTROL

Motivated by the novel coronavirus disease (COVID-19) pandemic, this paper aims to apply Gunter Stein's cautionary message of respecting the unstable to the problem of controlling the spread of an infectious disease. With this goal, we study the effect that delays and capacity constraints have in the test, trace, and isolate (TeTrIs) process, and how they impact its ability to prevent exponential disease spread. Our analysis highlights the critical importance of speed and scale in the TeTrIs process. Precisely, ensuring that the delay in the TeTrIs process is much smaller than the doubling time of the disease spread is necessary for achieving acceptable performance. Similarly, limited TeTrIs capacity introduces a threshold on the size of an outbreak beyond which the disease spreads almost like the uncontrolled case. Along the way, we provide numerical illustrations to highlight these points.