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

Markus Mueller; Peter Derlet; Christopher Mudry; Gabriel Aeppli

After the reboot at time t 1 = 0 further interventions will be necessary, as we assume that the reboot will have resulted in a positive growth rate k 1 . In subsequent interventions, the policymakers try to take measures that aim at reducing the growth rate to zero. Even if they had perfect knowledge of the current growth rate k(t), they would not succeed immediately since they do not know the precise quantitative effect of the measures they will take. Nevertheless, had they complete knowledge of k(t), our model assumes that they would be able to gauge their intervention such that the actual effect on k(t) differs at most by a factor between b and 1/b from the targeted value, which would reduce k(t) to 0. This and the assumption b ≥ 0.5 implies that, if α is large, so that k(t) is known with relatively high precision at the time of intervention, the growth rate k 2 is smaller than k 1 10 If the infected fraction of people is i(t), its growth rate iṡ i(t)/i(t) ≡ k(t) with the time derivative of i(t) denoted byi(t).