The COVID-19 epidemic of the novel coronavirus (severe acute respiratory syndrome SARS-CoV-2) has spread around the world. While different containment policies using non-pharmaceutical interventions have been applied, their efficiencies are not known quantitatively. We show that the doubling time T d(t) with the success s factor, the characteristic time of the exponential growth of T d(t) in the arrested regime, is a reliable tool for early predictions of epidemic spread time evolution and provides a quantitative measure of the success of different containment measures. The efficiency of the containment policy lockdown case finding mobile tracing (LFT) using mandatory mobile contact tracing is much higher than that of the lockdown stop and go policy proposed by the Imperial College team in London. A very low s factor was reached by the LFT policy, giving the shortest time width of the positive case curve and the lowest number of fatalities. The LFT policy was able to reduce the number of fatalities by a factor of 100 in the first 100 d of the COVID-19 epidemic, reduce the time width of the COVID-19 pandemic curve by a factor 2.5, and rapidly stop new outbreaks and thereby avoid a second wave to date. © 2020 IOP Publishing Ltd.