key: cord-0275537-ddd48ey1 authors: Nesteruk, I.; Rodionov, O. title: Effects of testing and vaccination levels on the dynamics of the COVID-19 pandemic and the prospects for its termination date: 2021-09-23 journal: nan DOI: 10.1101/2021.09.20.21263823 sha: 503c5137a35a934ad90d56f3136a13e490607695 doc_id: 275537 cord_uid: ddd48ey1 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. It was shown that vaccination can significantly reduce the likelihood of deaths. However, existing vaccines do not prevent new infections, and vaccinated individuals can spread the infection as intensely as unvaccinated ones. Therefore, 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 520 is exceeded, one can hope to stop the occurrence of new cases. To investigate the effectiveness of quarantine, testing and vaccination, different relative characteristics (calculated per capita) can be used. In particular, such values are regularly reported by COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU), [1] . The accumulated numbers of COVID-19 cases per capita (CC) was used in [2] to investigate the influence of demographic factors in European countries. In the end of June 2021 accumulated numbers of deaths per capita caused by coronavirus (DC) and the mortality rate DC/CC versus TC and TC/CC. The current dynamics of the pandemic is characterized by daily increases in the number of cases. The daily numbers of new COVID-19 cases per capita (DCC) was used in [3] to find some seasonal trends of the COVID-19 pandemic in the EU and some other countries. This characteristic and the daily numbers of new deaths per capita caused by coronavirus (DDC) are very important in order to investigate the efficiency of vaccinations. In particular, it was shown in [4] that rather high numbers of fully vaccinated people per capita (VC) did not protect the population of Israel against a new pandemic wave in the summer of 2021. In this paper we will try to find a correlation between DCC, DDC and VC values. are very random and demonstrate some weekly periodicity, we will use smoothed (averaged) values calculated and displayed by JHU with the use of figures registered during the previous 7 days. This smoothing procedure differs from one proposed in [5] [6] [7] , where the values registered in the nearest 7 days were used. We will use the linear regression to calculate the regression coefficients r and the coefficients a and b of corresponding best fitting straight lines, [8] : where x are TC, TC/CC, and VC values and y are CC, DC, DC/CC, DCC, DDC, and DDC/DCC values. We will use also the F-test for the null hypothesis that says that the proposed linear relationship (1) fits the data sets. The experimental values of the Fisher function can be calculated with the use of the formula: where n is the number of observations (number of countries and regions taken for statistical analysis); m=2 is the number of parameters in the regression equation, [8] . The corresponding experimental values ( , )/ C F k k F correspond to the most reliable hypotheses (see, e.g., [10] ). The results of the linear regression application are presented in Table 2 for European countries and by "circles" for other countries and regions. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 23, 2021. ; Only one country -Australia -exceeded these estimations for the critical values of the tests per case ratio (see last right "circles" in Fig. 2) . The corresponding CC and DC values in this country are very low (see blue and black "circles"). Nevertheless, new cases and deaths occur in Australia. This situation can be explained by a decrease in the number of tests. As of September 1, the daily number of tests per 1,000 population was 10,069 [1] . Taking the corresponding DCC value 48.306 from Table 1 , we obtain 208.4 as a recent value of the tests per case ratio. Cases per million (CC, blue), deaths per 100 million (DC*100, black), mortality rate (DC*10 7 /CC, red). Best fitting lines (1) are solid for European datasets and dashed for complete datasets. "Crosses" represent the European datasets, "circles" -figures for other countries and regions. In contrast to the values of DC, the ratio DC/CC does not show any visible correlation with the tests to case ratio TC*1000/CC especially for the complete datasets (in Table 2 , the corresponding value of the regression coefficient r is -0.0790). This statistical conclusion may seem strange at first glance, but the ratio DC/CC shows how many sick people die. That is, it is a characteristic of the ability of patients to resist the captured strain of the coronavirus and the level of medical care. Therefore, it should not depend on the number of tests performed to identify one infected patient. The effect of vaccination levels VC on the daily number of new cases DCC was much unexpected due to the practical lack of correlation. We can see in Table 1 the values of the correlation coefficients -0.1004 and 0.1245 for the European and complete datasets, respectively and 1 2 / ( , ) 1 C F F k k  . The same conclusion can be drawn from the best fitting blue lines shown in Fig. 3 . All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 23, 2021. ; The available statistical data show that new cases will appear even if the entire population of the earth is vaccinated. But vaccination significantly reduces the number of new deaths (see black lines in Figure 3) and attitudes of DDC/DCC (red lines). We can see also in Table 2 Table 2 ) we obtain the critical vaccination level 78.8% for the European dataset. For the complete dataset this figure is 90.7%. The black lines in Fig. 3 for European and complete datasets, respectively (see red lines in Fig. 3 ). Looking at Table 1 , we see that as of September 1, 2021, no European country has reached the appropriate critical level of vaccination 83.1%. The same can be said for other countries and regions shown in Table 1 . All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823 doi: medRxiv preprint It should be noted that the vaccination levels listed in Table 1 are calculated based on the full volume of populations (including children), so a further increase in VC values (in order to exceed critical figures) requires vaccination of children. Another disadvantage of existing vaccines is their ineffectiveness against new strains of coronavirus, because as mentioned above, new cases will continue to appear even with 100% vaccination. Here is a very illustrative example of Israel, which was experiencing a strong wave in September 2021, despite a fairly high level of vaccination (more than 63.3%). In particular, the daily number of new cases (DDC) exceeded the values registered before the start of vaccination, [4] . The emergence of new cases (even if they are not fatal) increases the likelihood of new more pathogenic strains, which can dramatically worsen the situation. Therefore, to overcome the pandemic, we should not rely only on vaccination. The presented statistical analysis shows that vaccinated individuals can become re-infected and are just as dangerous to others as those who have not been vaccinated (since the DCC values do not correlate with the vaccination level). Therefore, the introduction of special passports that remove restrictions for vaccinated persons is questionable. Having fresh PCR tests can be a more effective pass to crowded places in order to prevent the spread of infection. To discuss the possibilities of complete cessation of the pandemic, let us pay attention to the dependence of CC versus TC/CC for the complete data set shown by the blue dashed line in Fig. 2 . As mentioned earlier, the epidemic can be taken under complete control (CC values are close to zero), if the number of tests per case is high enough (TC*1000/CC > 520). Indeed, if every detected case is accompanied by testing of many possible contacted persons and isolation of the infected ones, then we have a chance to completely stop the spread of infection. For the case of coronavirus, the number of such tests is quite large. But as the situation in Australia shows, the appropriate level of testing can be achieved (see Fig. 2 ). Due to this the CC value in this country is 2193.25 which is much less than the corresponding figures for other countries and regions listed in Table 1 (for example, in the whole world, this value is 12.6 times higher). [1] ). Thus, at the beginning of the COVID-19 pandemic, the tests per case values were less than critical one, but in the summer of 2021 they exceeded the critical level. Apparently, this allows more or less effective control of the epidemic in Hong Kong at rather low vaccination level. For example, as of September 1, 2021 DCC=0.738 which is 111 times less than worldwide (see Table 1 ) and VC=46%. It seems that in mainland China, many more tests were performed per one laboratoryconfirmed case. Unfortunately, the data reported by JHU [1] allows us to calculate only two values 1078 (June 24, 2020) and 1891 (August 6, 2020). Such high levels of testing are likely to have led to complete control of the epidemic in China. The value DCC=0.019 (September 1, 2021, [1] ) is 4312 times lower than worldwide (see Table 1 ). Increasing the number of tests requires significant costs. But in the periods between pandemic waves (when the daily number of new cases is small), even poor countries can afford to do extensive testing of possible contacts and rapid isolation of infected people. If the number of tests per case everywhere exceeds 520, we will have a chance to stop the COVID-19 pandemic. A simple statistical analysis of the daily number of new cases (DCC) and deaths (DDC) per capita showed that vaccination can significantly reduce the likelihood of deaths (DDC/DCC values). However, existing vaccines do not prevent new infections, and vaccinated individuals can spread the infection as intensely as unvaccinated ones. Therefore, 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 ones. As existing vaccines are not able to prevent this, it All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823 doi: medRxiv preprint COVID-19 Data Repository by the Center for Systems Science and Engineering The impact of demographic factors on the accumulated number of COVID-19 cases per capita in Europe and the regions of Ukraine in the summer of 2021. medRxiv The impact of seasonal factors on the COVID-19 pandemic waves. medRxiv Comparison of the COVID-19 pandemics dynamics in Ukraine and Israel in the summer of 2021 COVID-19 pandemic dynamics. Springer Nature Visible and real sizes of new COVID-19 pandemic waves in Ukraine Innov Biosyst Bioeng. 2021 Detections and SIR simulations of the COVID-19 pandemic waves in Ukraine Applied regression analysis Comparison of the First Waves of the COVID-19 Pandemic in Different Countries and Regions remains to increase the number of tests per registered case (TC*1000/CC values). Statistical analysis showed that if the critical value of 520 is exceeded, one can hope to stop the occurrence of new cases.