The sharp increase in the number of new COVID-19 cases in late 2021 and early 2022, which occurred even in countries with high vaccination levels, has raised the question about the possibility of overcoming the pandemic only through vaccination. Averaged daily numbers of new COVID-19 cases and deaths per capita and their ratio were used to find links with the percentages of fully vaccinated people and boosters and the tests per case ratio. The datasets for European and some other countries and regions corresponding to February 01, 2022 were used. Simple linear and non-linear statistical methods showed that vaccinations can significantly reduce the likelihood of deaths and the increase in the tests per case ratio diminishes the number of infections. These conclusions are consistent with the previous study based on the data from September 01, 2021 (before the advent of the Omicron). However, the numbers of new daily Omicron cases per capita increase with the increase of the percentage of fully vaccinated people and boosters. It looks that removal of restrictions on the movement of vaccinated persons and the abolition of many quarantine restrictions have led to a sharp increase in the number of infections. To overcome the pandemic, the increase of the tests per case ratio and extension of quarantine restrictions are necessary.