Using random testing to manage a safe exit from the COVID-19 lockdown

Markus Mueller; Peter Derlet; Christopher Mudry; Gabriel Aeppli

Without feedback and control informed by a primary indicator, analogous to the temperature provided by the thermometer in the thermostat example, measurable in (near) real time, there is a huge lapse between policy changes and the observable changes in numbers of positively tested people. To relax restrictions safely, the frac- The key quantity measured by random testing is the growth rate k of infection numbers. If k exceeds a tolerable upper threshold κ + , restrictions are imposed. For k below a lower threshold κ − , and if infection numbers are below critical, restrictions are released. In the absence of a substantial influx of infected people from outside the country, and provided infection numbers are below a critical value, the optimal target of the growth rate is k = 0, corresponding to a marginally stable state, where infections neither grow nor decrease exponentially with time. If higher testing rates are available, the measured observables and control strategies can be geographically refined, particularly to avoid hotspots. tion of currently infected people must decrease to a level i * * such that a subsequent undetected growth during 10-14 days will not move it above the critical fraction i c manageable by the health-care system. The current situation where we are mainly looking at lagging secondary indicators, namely infection rates among symptomatic individuals or even deaths, is comparable to driving a car from the back seat and with knowledge only of the damage caused by previous collisions. To minimize harm to the occupants of the vehicle, driving very slowly is essential, and oscillations from a straight course are likely to be large.