key: cord-0851448-m19kklm9 authors: Nesteruk, I. title: Impact of vaccination and undetected cases on the COVID-19 pandemic dynamics in Qatar in 2021 date: 2021-06-01 journal: nan DOI: 10.1101/2021.05.27.21257929 sha: af283eb3c87a9674ed96fdd0135074a6be752a35 doc_id: 851448 cord_uid: m19kklm9 The third COVID-19 pandemic wave in Qatar was simulated with the use of the generalized SIR-model and the accumulated number of cases reported by Johns Hopkins University for the period: April 25 - May 8, 2021. Comparison with the SIR-curves calculated before for the second wave showed that the effect of mass vaccination is not evident during 4 months after its onset in December 2020. Additional simulations have demonstrated that many COVID-19 cases are not detected. The real accumulated number of cases can exceed the laboratory-confirmed one more than 5 times. This fact drastically increases the probability of meeting an infectious person and the epidemic duration. The COVID-19 pandemic dynamics in Qatar was simulated with the use of SEIR-model (susceptible-exposed-infected-removed) [1] and SEIRD-model (susceptible-exposed-infected-removeddead) [2] . Some recent SIR-simulations [3] were based on the dataset about the number of cases in December 2020, when the mass vaccination started in this country. In this study we will use the information about the accumulated number of cases from COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU), [4] . We will analyze the recent epidemic dynamics in Qatar and make some predictions taking into account the incompleteness of the statistical information with the use of method proposed in [5] . We will use two data sets regarding the accumulated numbers of confirmed COVID-19 cases V j , number of vaccinated people S j and number of vaccinations Q j in Qatar from JHU, [4] . These values and corresponding moments of time t j (measured in days) are shown in Table 1 . For SIR-simulations All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 1, 2021. ; https://doi.org/10.1101/2021.05.27.21257929 doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. we have used the values of V j and t j corresponding to the time period T c3 : April 25 - May 8, 2021 during the third epidemic wave in Qatar. Other values presented in Table 1 and datasets available in [3] were used only for comparisons and verifications of the calculations. The classical SIR model for an infectious disease [6] [7] [8] was generalized in [5, 9] Here S is the number of susceptible persons (who are sensitive to the pathogen and not protected); I is the number of infectious persons (who are sick and spread the infection ); and R is the number of removed persons (who no longer spread the infection). It must be noted that I(t) is not the number of active cases. People can be ill (among active cases), but isolated. In means, that they don't spread the infection anymore. There are many people spreading the infection but not tested and registered as active cases. The use of number of active cases as I(t) in some papers a principal mistake which may lead to incorrect results. Parameters i  and i  are supposed to be constant for every epidemic wave. To determine the initial conditions for the set of equations (1)-(3), let us suppose that at the beginning of every epidemic wave * i t : In [5, 9] the set of differential equations (1)-(3) was solved by introducing the function when the number of persons spreading the infection will be less than 1) can be found in [5, 9] . All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 1, 2021. ; https://doi.org/10.1101/2021.05.27.21257929 doi: medRxiv preprint For many epidemics (including the COVID-19 pandemic) we cannot observe dependencies ( ), ( ) S t I t and ( ) R t but observations of the accumulated number of cases V j corresponding to the moments of time t j provide information for direct assessments of the dependence ( ) V t . In the case of a new epidemic, the values of its parameters are unknown and must be identified with the use of limited data sets. For the second and next epidemic waves (i > 1), the moments of time * i t corresponding to their beginning are known. Therefore the exact solution [5, 9] depend only on five parameters -, , , , when the registered number of victims V j is a random realization of its theoretical dependence (4). The real number of COVID-19 cases is much higher than the number of laboratory-confirmed patients [5, [10] [11] [12] [13] [14] [15] , since many patients have no symptoms or make no tests. If we assume, that data set V j is incomplete and there is a constant coefficient 1 i   , relating the registered and real number of cases during the i-th epidemic wave: then the number of unknown parameters increases by one. The values V j , corresponding to the moments of time t j , the exact solution [5, 9] and relationship (5) can be used to find the optimal values of the parameters , , , , , providing the maximum value of the correlation coefficient r i (see details in [5, 16] ). First we have calculated the optimal vales of parameters for the third wave of the COVID-19 pandemic in Qatar assuming that the dataset V j and t j reflects the real number of cases (i.e., we supposed that 3 1   ). The results are shown in Table 2 (third column). The last column of the Table 2 represents the characteristics of the second wave calculated in [3] for 2 1   . It can be seen that the optimal values of parameters , , All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 1, 2021. as follows: Values of the derivative (8) are shown in Fig. 1 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 1, 2021. 1 i   . 10 -dashed; derivatives dV/dt (eq. (6)) multiplied by 100 -dotted. Markers show accumulated numbers of laboratory-confirmed cases V j (from Table 1 and [3] ) and derivatives. Red "Circles" correspond to the accumulated numbers of cases taken for calculations of the third wave (during period of time T c3 ); blue "stars" -number of cases beyond T c3 . "Crosses" show the first derivatives (eq. (8)) multiplied by 100. Blue "stars" in Fig. 1 show the laboratory-confirmed cases V j (from Table 1 and corresponding corresponding to values taken for SIR simulations of the third epidemic wave in Qatar). It can be seen that the registered number of cases deviates from the theoretical curve for the second wave (compare the black line and "stars" in Fig. 1 ). The V(t)=I(t)+R(t) curve for the third wave (calculated with the use of fresher dataset) is in good agreement with the accumulated number of cases confirmed after mid-March 2021 (compare the red line and "stars" in Fig. 1 ). Assuming that the dataset V j does not reflect the real number of cases, we have calculated the optimal value of the visibility coefficient 3 (5) and other optimal vales of parameters for the third wave of the COVID-19 pandemic in Qatar. The results are shown in Table 2 (second column). It can be seen that the correlation coefficient for the invisible wave 3 is higher than for its visible part. There is a huge difference in the optimal values of parameters , , Table 2 ). Red lines in Fig.2 represent the SIR curves for the invisible dynamics of the third epidemic wave in Qatar. Solid line shows the number of victims V(t)=R(t)+I(t), dashed line -the number of infectious All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 1, 2021. ; https://doi.org/10.1101/2021.05.27.21257929 doi: medRxiv preprint persons I(t) multiplied by 10 and dotted line -the derivative (6) multiplied by 100. The accumulated numbers the laboratory-confirmed cases V j (shown by blue "stars" and red "circles") are much lover than the theoretical estimation of real number of cases V(t)=R(t)+I(t) (shown by the solid red line). To check the reliability of the method and the results of calculations the accumulated number of laboratory-confirmed cases V j (listed in Table 1 ) was smoothed with use of formula (7) (7) and (8) Numbers of victims V(t)=I(t)+R(t) -solid lines; numbers of infected and spreading I(t) multiplied by 10 -dashed; derivatives dV/dt (eq. (6)) multiplied by 100 -dotted. Markers show accumulated numbers of laboratory-confirmed cases V j (from Table 1 ) and derivatives. Red "Circles" correspond to the accumulated numbers of cases taken for calculations of the third wave (during period of time T c3 ); blue "stars" -number of cases beyond T c3 . "Crosses" show the first derivatives (eq. (8)) multiplied by 3 100 . The blue line represents smoothed accumulated number of laboratory-confirmed cases (7) multiplied by 3  . All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 1, 2021. ; https://doi.org/10.1101/2021.05.27.21257929 doi: medRxiv preprint The mass vaccination started in Qatar in late December 2020. The corresponding numbers of vaccinated people S j and vaccinations Q j are shown in Fig. 2 by "green" and "yellow" markers, respectively. Despite the relatively rapid rate of vaccination (in May 2021, the number of fully vaccinated people Q j -S j approached half of the population), Qatar experienced the new wave of pandemics with a sharp increase in the number of patients in March-April 2021 (see blue "crosses" in Fig. 1 ). According to the forecast of the previous second wave (made in [3] using data before vaccination), the number of cases of should stabilize rapidly in 2021 (see the black solid line in Fig. 1 ). We will probably see the effect of vaccination only in June 2021. At least the latest data on the daily number of new cases have already become less than the theoretical estimates for the third wave (compare "blue" crosses and red dotted lines in Figs. 1 and 2) . The calculated coefficient of epidemic visibility 3 in Slovakia was also approximately 1% of population [17] . Ignoring information about the large number of unreported cases can lead to incorrect recommendations for quarantine restrictions and overly optimistic forecasts of the COVID-19 pandemic duration. For example, the information about the real dependence I(t) is important to estimate the probability of meeting an infected person with the use of simple formula, [18] : where pop N is the volume of population. As of the end of May, 2021 the theoretical estimation yields the value I  of 10,000 (see the dashed line in Fig. 2 ). Then the probability p can be estimated as 0.0034 for Qatar. If only officially registered cases are taken into account, the corresponding probability will be approximately 5.3 times lower. If current trends continue, new cases in Qatar will cease to be registered in January 2022 (see the third column in Table 2 ). But the invisible cases will continue for another two months (see the second column in Table 2 ). During this long period, new strains of the coronavirus may emerge and cause a new epidemic wave, which will be unexpected, as the visible part of the epidemic seemed to have been overcome. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 1, 2021. ; https://doi.org/10.1101/2021.05.27.21257929 doi: medRxiv preprint The application of generalized SIR model to the new COVID-19 pandemic wave in Qatar demonstrated once more its effectiveness in predictions of epidemic dynamics and estimations of the vaccination efficiency. The parameter identification procedure allowed calculating the coefficients of data incompleteness (approximately 5.3 in the end of April 2021). New simulations with the use of fresher datasets are necessary to update the estimation of the vaccination efficiency in Qatar. Probably, real sizes of the pandemic in other countries are also much large than the number of registered cases. Thus reassessments of the COVID-19 pandemic dynamics are necessary, to avoid new unexpected waves. 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