ABSTRACT
In this paper, we investigate the effectiveness of COVID-19 vaccination in controlling the infectivity and mortality of the SARS-CoV-2. Two major variants Delta and Omicron are investigated respectively. The main method used in the research is the multifractal detrended fluctuation analysis (MF-DFA). We use Δ α as the evaluation of control effectiveness. In the transmission stages of Delta and Omicron, we observe whether Δ α shows a downward trend by gradually expanding the length of time series. Vaccine effectiveness is evaluated using a time series of newly diagnosed patients and newly reported deaths. Data samples are taken from 9 different countries. According to the obtained results, the vaccine controls infectivity and mortality of the virus in the Delta transmission stage, but infectivity control is less effective than mortality. In the Omicron transmission stage, the immune effect of the vaccine is not obvious, which may be related to the high infectivity of Omicron. However, the vaccine is still effective in controlling mortality. We also find that the immune effect of vaccine on Omicron was lower than that of Delta. Finally, we observe that the immune effect of the vaccine in 'Poland' was abnormal. By analyzing the vaccination curve, we conclude that in 'Poland', when the growth rate of vaccination rate slowed down, the immune effect of the vaccine was very poor in terms of pathogenicity and lethality. Therefore, we suggest that all countries should continue to strengthen the vaccination rate. A higher or faster growth rate of vaccination rate will help control the infectivity and mortality rate, especially in the effectiveness of controlling mortality. Our research can be used to evaluate the effectiveness of vaccines for epidemic prevention and control, the formulation of epidemic prevention measures and vaccination policies for different countries with respect to their current pandemic situation accordingly.