The Covid-19 epidemic of the novel coronavirus (severe acute respiratory syndrome [SARS]-CoV-2) has been spreading around the world. While different containment policies using nonpharmaceutical interventions have been applied, their time evolution and efficiency are not known quantitatively. We show here that the measure of the doubling time Td(t) is a reliable tool for early predictions of epidemic spread time evolution following mitigation, which is needed for planning methods to overcome critical health care need. The doubling time Td(t) curves over the epidemic dome full time width provide a quantitative measure of the success of different containment measures. The efficiency of the Lockdown case Finding mobile Tracing (LFT) policy using modern technologies is found to be much higher than the traditional Lockdown Stop and Go (LSG) policy using the success s factor. A low s factor, the characteristic time of the exponential growing Td(t) in the arrested regime, was reached by LFT policy giving the lowest number of deaths and the shorter time width of the epidemic dome. The record for the largest number of fatalities in USA is correlated with the largest s factor in the near threshold regime when any containment measures were enforced by government in due time. LFT policy has been able to reduce both intensity and time width of the Covid-19 pandemic dome achieving both a low number of fatalities and lower economic losses.