The main objective of this paper is to answer the following question: are the containment measures imposed by the majority of world governments effective and sufficient to stop the epidemic of COVID-19? Thanks to a mathematical model that we have developed, we have been able to show that containment measures appear to have slowed the growth of the outbreak. Nevertheless these measures remain only effective as long as a very large fraction of the population remains confined. This means that if no further action is taken, a new wave of contamination larger than the former is expected very shortly after the end of containment date. The combined measures of the large scale test of detection of infected individuals and the social distancing were shown to be effective to overcome the outbreak. While taking separately the both latter measures is not sufficient to prevent a second wave.