Effects of testing and vaccination levels on the dynamics of the COVID-19 pandemic and the prospects for its termination

A simple statistical analysis of the accumula ted 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 s hown that vaccination can significan tly reduce the likelihood of deaths. However, existing vaccines do not prevent new infec tions, and vaccinated individuals can spread the infection as intensely as unvaccinated ones. Therefore, it is too early to lift qua rantine restrictions in Europe and most other countries. The constant appear ance of new cases due to re-infection increases the likelihood of new coronavirus strains, including very dangerous. As existing v accines are not able to prevent this, it remains to increase the number of tests per registered case. If th e critical value of 520 is exceeded, one can hope to stop the occurrence of new cases.

COVID-19 pandemic, epidemic dynamics in Europe, statistical methods.

To investigate the effectiveness of quarantin e, 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 Syst ems Science and Engineer ing (CSSE) at Johns Hopkins University (JHU), [1]. The accumulated numb ers of COVID-19 cases per capita (CC) was used in [2] to investigate the influence of demographic f actors in European countries . In the end of June 2021 the CC values varied more than 9 times for different European c ountries but showed no visible dependencies on the volume of population, its density, and the level of urbanization. In this paper we will try to find some statistical correlation between CC values and the accumulated num ber of tests per capita (TC) and the tests per cases ratio TC/CC. We will try also to find similar relationships for the 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 preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. 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 charac terized by daily increases in the number of cases. The daily numbers of new COVID-19 cases pe r 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 vaccina tions. In particular, it was shown in [4] that rather high numbers of fully vaccinated people per capita (VC) did not pr otect the population of Isra el 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. Data, the linear regression and Fisher test Country Total cases per million CC Total death per million DC Total tests per thousand TC People fully vaccinated, %, VC New cases per million, smoothed DCC New deaths per million, smooth. DDC European countries Monaco 81250 835.02 no data 57.07 1 173.511 0 Holy See (Vatican City) 33251.232 no data no data no data 0 0 Malta 70442.161 857.036 2321.107 80.27 94.116 1.111 San Marino 156748.02 2646.281 no data 70.49 163.817 0 Netherlands 115262.92 1069.871 736.14 2 62.642 152.897 0.516 Belgium 102086.65 2182.021 1614.388 70.14 176.822 0.418 United Kingdom 100531.05 1950.911 3590.956 63.08 492.479 1.556 Liechtenstein 85690.385 1542.322 1624.614 53.55 115.768 0 Luxembourg 119568.88 1307.47 5400.155 56.18 133.222 0 Germany 47435.24 1099.66 838.0142 60.34 116.255 0.293 Italy 75313.524 2141.716 1397.101 61.1 104.34 0.89 Switzerland 89824.971 1251.449 1079.174 51.23 289.779 0.82 Andorra 194508.36 1680.585 2709.918 2 54.08 59.098 0 Denmark 59838.969 444.842 6874.115 72.59 147.027 0.319 Czech Republic 156601.03 2834.99 no data 53.6 18.556 0.226 Poland 76435.59 1993.756 513.568 49.8 6.675 0.11 Portugal 102232.48 1746.374 1682.166 75.37 191.4 1.166 Slovakia 72357.046 2297.863 7527.671 39.81 21.897 0.026 Albania 51295.644 870.539 256.537 3 22.58 298.55 0.895 Austria 76318.424 1191.52 8492.748 57.82 157.563 0.079 France 101653.62 1702.542 no data 60.19 233.095 1.672 Hungary 84338.524 3120.043 636.628 57.2 17.705 0.059 Turkey 75400.291 670.251 901.9 43.94 232.817 3.004 Slovenia 128907.03 2140.737 699.719 43.58 227.681 0.481 Moldova 66626.077 1591.938 393.622 1 17.29 81.226 0.923 Spain 104008.15 1807.073 1186.8214 72 142.652 2.39 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 thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: medRxiv preprint CC DC TC VC DCC DDC Serbia 112611.98 1073.833 741.032 41.31 369.204 1.554 Romania 57518.879 1808.418 477.1551 26.89 54.05 1.031 North Macedonia 85179.009 2863.644 553.002 5 25.88 399.42 14.336 Greece 56971.017 1318.034 1506.965 55.43 285.9 2.893 Bosnia and Herzegovina 65807.17 3007.545 350.723 13.06 9 161.967 2.495 Croatia 91826.187 2042.798 623.2756 39.68 133.629 0.98 Ireland 71090.272 1025.908 1348.36 68.09 341.367 0.573 Ukraine 54916.644 1312.863 276.267 8.99 49.815 1.479 Bulgaria 66334.622 2747.709 620.083 1 17.12 223.483 6.981 Belarus 51174.183 401.467 827.889 14.152 157.02 1.195 Montenegro 184628.32 2757.738 no data 29.45 959.886 8.416 Lithuania 111355.9 1698.6 1723.318 56.23 220.882 3.399 Latvia 76652.951 1381.409 1788.741 7 40.96 120.136 0.689 Estonia 107428.53 975.711 1335.17 41.27 261.526 0.862 Sweden 111013.72 1446.04 no data 56.21 2 102.487 0.253 Norway 29605.742 150.394 1318.59 58.07 253.402 0.209 Finland 23044.824 185.64 1201.377 51.1 108.809 0.309 Iceland 31616.962 96.109 1715.983 76.82 214.269 1.248 Other countries and regions United States 118336.96 1929.465 1604.422 51.91 503.381 4.186 North America 79327.442 1643.263 no data 42.43 338.245 3.973 Argentina 113822.04 2455.936 293.9 32.42 112.357 3.255 Brazil 97218.938 2715.737 148.213 8 29.68 105.93 3.007 South America 85023.252 2605.171 no data 31.06 76.457 2.336 South Africa 46420.892 1373.972 275.411 10.23 154.656 4.823 Africa 5694.404 143.37 no data 2.86 20.617 0.535 India 23580.97 315.434 375.471 10.9 30.696 0.324 Israel 123209.17 806.164 2675.281 62.52 1058.958 2.893 Japan 11991.372 128.131 166.789 46.85 161.421 0.434 South Korea 4978.074 44.888 241.129 31.74 33.647 0.128 Qatar 79477.254 205.424 856.443 73.44 65.859 0.049 Asia 15035.556 222.955 no data 28.91 54.181 0.868 Australia 2193.25 39.514 1233.936 28.37 48.306 0.166 World 27737.424 575.503 no data 27.3 81.926 1.232 Figures corresponding different days in 2021: 1 09-02; 2 08-29; 3 06-13; 4 08-26; 5 08-30; 6 08-31; 7 08-27; 8 05-24; 9 09-07. Table 1. Accumulated and daily characteristics of the COVID-19 pandemic dynamics in European and some other countries and regions as of September 1, 2021 (figures corresponding to other days in May-September 2021 are specified in notes), [1] We will use the data sets regarding the relative characteristics (per capita) reported by JHU as of September 1, 2021, [1]. The figures corresponding to the version of the JHU table available on 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 thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: medRxiv preprint September 12, 2021 are presented in Table 1. We cannot fix the date Se ptember 12 for all the data, since many figures appear in the JHU table with the delay. The accumulated characteristics: CC (number of cases per million), DC (number of deaths per m illion), TC (number of tests per thousand), VC (percentage of fully vaccinated people) are taken without smoothing. Since daily characteristics DCC (new cases per million) and DDC (new deaths per million) are very random and demonstrate some weekly peri odicity, we will use smoothed (averaged) values calculated and displayed by JHU with the use of figures register ed during the previous 7 days. This smoothing procedure differs from one proposed in [5-7], 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]: ya b x  (1) 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 hyp othesis that says that the proposed linear relationship (1) fits the data sets. The experimental values of the Fish er function can be calculated with the use of the formula: 2 2 () (1 )( 1) rnmF rm    (2) 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 corres ponding experimental values F have to be compared with the critical values 12(, )CF kk of the Fisher function at a desired significance or confidence level ( 1 1km , 2kn m , see, e.g., [9]). If 12(, ) / 1CFkk F  , the null hypothesis is not supported by the results of observa tions. The highest values of 12(, ) /CF kk F correspond to the most reliable hypotheses (see, e.g., [10]).

The results of the linear regr ession application are presente d in Table 2 and Figs. 1-3. We have used the data sets corres ponding to the European countries and complete datasets with the information about some other countries and regions. Thus, we have two different numbers of observations n for every application of the linear relationship (1 ). Due to the lack of some data, the numbers n are different for different relationshi ps (e.g., versus TC and versus VC ). Corresponding values of the regression coefficients r, coefficients a and b; values of the Fisher function F, 12(, )CF kk and 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 thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: medRxiv preprint 12/( , )CF Fkk are shown in Table 2. The best fitting lines (1 ), calculated with the use of corresponding values a and b are shown in Figs. 1-3 by solid lines for European datasets and by dashed lines for complete datasets. The values CC, DC, CC/DC, DCC, DDC, and DDC/DCC are represented by “crosses” for European countries and by “circles” for other countries and regions. Fig.1. Characteristics of the COVID-19 pandemic versus number of tests per million (TC*1000) accumulated up to September 1, 2021. Cases per million (CC, blue), deaths pe r 100 million (DC*100, black), mortality rate (DC*107/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. Table 2 and Fig. 1 illustrate th at there is no visible correlation between all the relative accumulated characteristics (CC, DC and DC/CC) and the accumulated number of tests per capita (TC), since 12/( , ) 1CFFkk  for all 6 calculations (see the rows in Table 2 corresponding to Fig.1). Statistical analysis did not confirm the common view that more tests per capita can better identify patients and lead to an increase in CC and DC values. A very weak growth trend with increasing number of tests we see for CC values (see blue lines in Fig. 1). For values DC and DC/CC, black and re d lines illustrate opposite trends. This probably triggers the fact that more tests can detect and isolate patients more quickly, slowing the spread of infection and the number of deaths. The competition of these two tendencies results in an almost imperceptible correlation. It looks that it is impossible to stop the pandemic by increasing the number of tests per capita. In comparison, the increase of the relative characteristic - number of tests per case ratio (TC*1000/CC) – always diminishes the CC, DC and DC/CC values (see line s in Fig. 2). Moreover, 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 thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: medRxiv preprint visible correlations with TC/CC were revealed for CC and DC values ( 12/( , ) 1CFFkk  only in the relationship CC versus TC/CC for Europ ean countries). This fact allows us to conclude that the increase in the tests per case ratio could st op the pandemic. To ca lculate the corresponding TC /CC values lets us put in eq. (1) y=0 and obtain the corresponding x0 value as follows: 0 ax b  (3) Number of Figure, relationship Num- ber of ob- ser va- tions n Correlation coefficient r Optimal values of parameters a in eq. (1) Optimal values of parameters b in eq. (1) Experimental value of the Fisher function F, eq. (2), m=2 Critical value of Fisher Function F c(1,n-2) for the confidence level 0.1, [9] F c/F 37 0.0952 7.8115e+04 1.5147 0.3202 2.86 0.1120 1, CC versus TC 47 0.1728 7.1474e+04 3.3914 1.3848 2.84 0.4876 37 -0.1176 1.5699e+03 -0.0454 0.4906 2.86 0.1715 1, DC versus TC 47 -0.0478 1.4190e+03 -0.0218 0.1031 2.84 0.0363 37 -0.1793 0.0205 -9.1515e-07 1.1620 2.86 0.4063 1, DC/CC versus TC 47 -0.1565 0.0194 -8.3788e-07 1.1293 2.84 0.3977 37 -0.2471 8.7751e+04 -2.7460e+05 2.2752 2.86 0.7955 2, CC versus TC/CC 47 -0.3580 8.2349e+04 -1.5841e+05 6.6143 2.84 2.3290 37 -0.3191 1.7042e+03 -8.6173e+03 3.9668 2.86 1.3870 2, DC versus TC/CC 47 -0.3161 1.4969e+03 -3.2532e+03 4.9951 2.84 1.7588 37 -0.2460 0.0210 -0.0877 2.2544 2.86 0.7883 2, DC/CC versus TC/CC 47 -0.0790 0.0184 -0.0095 0.2826 2.84 0.0995 43 -0.1004 234.6744 -0.8581 0.4171 2.85 0.1464 3, DCC versus VC 58 0.1245 136.6035 1.2095 0.8821 2.8 0.3150 43 -0.3730 4.1071 -0.0521 6.6256 2.85 2.3248 3, DDC versus VC 58 -0.2972 3.2549 -0.0359 5.4255 2.8 1.9377 43 -0.5087 0.0194 -2.3335e-04 14.3156 2.85 5.0230 3, DDC/DCC versus VC 58 -0.5855 0.0227 -2.8822e-04 29.2106 2.8 10.4324 Table 2. Optimal values of parameters in eq. (1), correlation coefficients and the results of Fisher test applications. Application of formula (3) for 3 cases with 12/( , ) 1CFFkk  , yields the result that new COVID-19 cases in the world coul d stop when TC*1000/CC > 520 (see the blue dashed line in Fig. 2); deaths in the world could disappear at test per case ratio greater than 460 (see the black dashed line); the critical value for the deaths in Europe is TC*1000/CC = 198 (see the black solid line). 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 thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: medRxiv preprint Only one country – Australia – exceeded these estimations for the critical values of the tests per case ratio (see last right “circle s” in Fig. 2). The corresponding CC and DC values in this country are very low (see blue and black “circles”). Neverthele ss, new cases and deaths occur in Australia. This situation can be explained by a decreas e in the number of tests. As of September 1, the daily number of tests per 1,000 population was 10,069 [1]. Taking th e corresponding DCC value 48.306 from Table 1, we obtain 208.4 as a recent value of the tests per case ratio. Fig. 2. Characteristics of the COVID-19 pandemic versus tests per case ratio (TC*1000/CC) accumulated up to September 1, 2021. 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 th e complete datasets (in Table 2, the corresponding value of the regression coefficient r is -0.0790). This statistical conc lusion may seem strange at first glance, but the ratio DC/CC shows how many sick people di e. That is, it is a characteristic of the ability of patients to resist the captured strain of the cor onavirus 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 th e daily number of new cases DCC was much unexpected due to the practical lack of correlation. We can see in Tabl e 1 the values of the correlation coefficients -0.1004 and 0.1245 for the European and complete datasets, respectively and 12/( , ) 1CFFkk  . The same conclusion can be drawn from th e 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 thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: medRxiv preprint 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 deat hs (see black lines in Figure 3) and attitudes of DDC/DCC (red lines). We can see also in Table 2 that 12/( , ) 1CFFkk  for both datasets. Large values of 12/( , )CF Fkk calculated for the relationship DDC/DCC versus VC show that vaccinated infected persons will most likely not die, i.e. the course of the disease will not be very severe. Fig. 3. Smoothed daily characteristics of the COVID-19 pandemic versus percentage of fully vaccinated people (VC) as of September 1, 2021. New cases per million (DCC, blue), new deaths pe r 100 million (DDC*100, black), daily mortality rate (DDC*104/DCC, red). Best fitting lines (1) are solid fo r European datasets and dashed for complete datasets. “Crosses” represent the European datasets, “circles” – figures for other countries and regions. We can use eq. (3) in order to estimate the critical values of the vaccination level VC when the new deaths cease to appear. Taking the values of a=4.1071 and b=-0.0521 corresponding to the relationship DDC versus VC (see Table 2) we obtain the critical vaccination level 78.8% for the European dataset. For the complete dataset th is figure is 90.7%. The black lines in Fig. 3 illustrate these critical values. The most reliable relationships DDC/DCC ve rsus VC yield the critic al values 83.1% and 78.8% 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 reach ed 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 thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: 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 in crease 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, despit e 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 emerge nce of new cases (even if they ar e not fatal) increases the likelihood of new more pathogenic strains, which can dramatica lly 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 vaccin ated (since the DCC values do not correlate with the vaccination level). Therefore, th e 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. Many EU countries are ready to lift all coronavirus restrictions and Denmark has already done this on September 17, 2021, [11]. The obtained results al low us to estimate the risks connected with it. First, as mentioned earlier, even 100 percent vaccination does not save from the emergence of new waves. Unfortunately, the probability of death in case of infection (daily deaths per case ratio DDC/DCC) remains high due to the fact that the current levels of vaccination are less th an the critical values calculated in the previous section. For example, in Denmark, the vaccination rate VC on September 16, 2021 was 76.38% and 3 deaths caused by coronavirus were registered. Putting this figure into eq. (1) with corresponding values of coefficients a and b for European case from Table 2: (DDC/DCC) = 0.0194 - 2.3335e-04*(VC) (4) we can obtain DDC/DCC =0.0016. Thus, for every t housand new cases of infe ction (the number of which may become quite large), approximately 1.6 deaths could be expected in Denmark. The results obtained in this study do not in any way deny the need for vaccinations. On the contrary, equation (4) shows that the mortality rate can be significantly reduced with a high percentage of vaccinated persons. In the example of Denmark, we s ee that vaccinations have made it possible to reduce mortality rate DDC/DCC by about 12 times (DDC/DCC =0.0194 at VC=0%). But, unf ortunately, it will not be possible to completely stop the COVID-19 pa ndemic with the use of existing vaccines, since DCC values do not correlate with the vaccination level VC. 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 thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: medRxiv preprint To discuss the possibilities of complete cessatio n of the pandemic, let us pay attention to the dependence of CC versus TC/CC for the complete data set shown by the blue da shed line in Fig. 2. As mentioned earlier, the epidemic can be taken under comp lete 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). Hong Kong and mainland China have even lower CC values: 1603.776 and 65.772, respectively (as of September 1, 2021). The test per case ratios were rather high for Hong Kong: 300.8 (January 31, 2020); 222.9 (July 31,2 020); 680.4 (August 31, 2021); all figures were calculated with the use of information about accumulated numbers of tests and cases available in [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 vaccinati on 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 laboratory- confirmed 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 ne w cases is small), even poor coun tries can afford to do extensive testing of possible contacts and ra pid 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 num ber of new cases (DCC) and deaths (DDC) per capita showed that vaccination can significantly reduce th e likelihood of deaths (DDC/DCC values). However, existing vaccines do not prevent new infec tions, and vaccinated individuals can spread the infection as intensely as unvaccinated ones. Therefore, it is too early to lift qua rantine 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 thisthis version posted September 23, 2021. ; https://doi.org/10.1101/2021.09.20.21263823doi: medRxiv preprint remains to increase the number of tests per regist ered 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.

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