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

Markus Mueller; Peter Derlet; Christopher Mudry; Gabriel Aeppli

where k(t) is the instantaneous growth rate and Φ(t) accounts for infections arising from people crossing the national border. For simplicity, we set this influx to zero in this paper, in which case k(t) =U (t)/U (t) with the short-hand notationU (t) for the time derivative on the left-hand side of (5). An equation of the form (5) is usually part of a more refined epidemiological model [12] [13] [14] that accounts explicitly for the recovery or death of infected persons. For our purpose, the effect of these has been lumped into an overall time-dependence of the rate k(t). For example, it evolves as the number of immune people grows, restrictive measures change, mobility is affected, new tracking systems are implemented, hospitals reach their capacity, testing is increased, etc. Nevertheless, over a short period of time where such conditions remain constant, and the fraction of immune people does not change significantly, we can assume the effective growth rate k(t) to be piecewise constant in time. 8 We will exploit this below.