Data collected in the Global COVID-19 Trends and Impact Surveys (UMD Global CTIS), and data on variants sequencing from GISAID, are used to evaluate the impact of the Omicron variant (in South Africa and other countries) on the prevalence of COVID-19 among unvaccinated and vaccinated population, in general and discriminating by the number of doses. In South Africa, we observe that the prevalence of COVID-19 in December (with strong presence of Omicron) among the unvaccinated population is comparable to the prevalence during the previous wave (in August-September), in which Delta was the variant with the largest presence. However, among vaccinated, the prevalence of COVID-19 in December is much higher than in the previous wave. In fact, a significant reduction of the vaccine efficacy is observed from August-September to December. For instance, the efficacy drops from 0.81 to 0.30 for those vaccinated with 2 doses, and from 0.51 to 0.09 for those vaccinated with one dose. The study is then extended to other countries in which Omicron has been detected, comparing the situation in October (before Omicron) with that of December. While the reduction measured is smaller than in South Africa, we still found, for instance, an average drop in vaccine efficacy from 0.53 to 0.45 among those vaccinated with two doses. Moreover, we found a significant negative (Pearson) correlation of around -0.6 between the measured prevalence of Omicron and the vaccine efficacy.