A simple statistical analysis of the accumulated and daily numbers of new COVID-19 cases and deaths per capita was performed with the use of recent datasets for European and some other countries and regions in order to find correlations with the testing and vaccination levels. It was shown that vaccination can significantly reduce the likelihood of deaths. However, existing vaccines do not prevent new infections. It looks that vaccinated individuals can spread the infection as intensely as unvaccinated ones and it is too early to lift quarantine restrictions in Europe and most other countries. The constant appearance of new cases due to re-infection increases the likelihood of new coronavirus strains, including very dangerous. As existing vaccines are not able to prevent this, it remains to increase the number of tests per registered case. If the critical value of the tests per case ratio (around 520) is exceeded, one can hope to stop the occurrence of new cases.