key: cord-0741292-y108e2pz authors: Nesteruk, I. title: Visible and real sizes of the COVID-19 pandemic in Ukraine date: 2021-03-27 journal: nan DOI: 10.1101/2021.03.19.21253938 sha: 34ab42b78280a5bd668105985acb032be9283022 doc_id: 741292 cord_uid: y108e2pz To simulate how the number of COVID-19 cases increases versus time, various data sets and different mathematical models can be used. In particular, previous simulations of the COVID-19 epidemic dynamics in Ukraine were based on smoothing of the dependence of the number of cases on time and the generalized SIR (susceptible-infected-removed) model. Since real number of cases is much higher than the official numbers of laboratory confirmed ones, there is a need to assess the degree of data incompleteness and correct the relevant forecasts. We have improved the method of estimating the unknown parameters of the generalized SIR model and calculated the optimal values of the parameters. It turned out that the real number of diseases exceeded the officially registered values by about 4.1 times at the end of 2020 in Ukraine. This fact requires a reassessment of the COVID-19 pandemic dynamics in other countries and clarification of world forecasts. The studies of the COVID-19 pandemic dynamics are complicated by incomplete information about the number of patients (e.g., reported by WHO [1] ), a very large percentage of whom are asymptomatic. In the early stages of the pandemic, there was also a lack of tests and knowledge about the specifics of the infection spread. Because of this, there are more and more evidences of COVID-19 patient appearances before the first officially-confirmed cases [2] [3] [4] [5] [6] . These hidden periods of the epidemics in different countries and regions were estimated in [7] [8] [9] [10] [11] with use of the classical SIR model [12] [13] [14] and the statistics-based method of the parameter identification developed in [15, 16] . In particular, first COVID-19 cases probably have appeared already in August 2019 [9] [10] [11] . For Ukraine, different simulation and comparison methods were based on official accumulated number of laboratory confirmed cases [17, 18] (these figures coincided with the official WHO data sets [1] , but WHO stopped to provide the daily information in August 2020) and the data reported by Johns We will use the data set regarding the accumulated numbers of confirmed COVID-19 cases in Ukraine from national sources [17, 18] . The corresponding numbers V j and moments of time t j (measured in days) are shown in the supplementary [30] ). Nevertheless, the special simulations will demonstrate a significant incompleteness of both data sets. The classical SIR model for an infectious disease [12] [13] [14] was generalized in [11, [27] [28] [29] [30] Here S is the number of susceptible persons (who are sensitive to the pathogen and not protected); I is the number of infected persons (who are sick and spread the infection); and R is the number of removed persons (who no longer spread the infection; this number is the sum of isolated, recovered, dead, and infected people who left the region). 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 [11, [27] [28] [29] [30] ] the set of differential equations (1)-(3) was solved by introducing the function corresponding to the number of victims or the cumulative confirmed number of cases. 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 . The corresponding analytical formulas for this exact solution can be written as follows:   Thus, for every set of parameters , , , i i i i N I R  and a fixed value of V , integral (8) can be calculated and the corresponding moment of time can be determined from (7). Then functions I(t) and R(t) can be easily calculated with the use of formulas (9) . The saturation levels i (corresponding the infinite time moment) and the final day of the i-th epidemic wave (corresponding the moment of time when the number of persons spreading the infection will be less then 1) can be calculated with the use of equations available in [11, [27] [28] [29] [30] . 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 (7)-(9) depend only on five parameters -, , , , when the registered number of victims V j is the random realization of its theoretical dependence (6). 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: the number of unknown parameters increases by one. Then the values V j , corresponding to the moments of time t j and relationship (10) (7) which can be rewritten as follows: We can calculate the parameters  and  , by treating the values * ( , , , , , ) corresponding time moments t j as random variables. Then we can use the observations of the accumulated number of cases and the linear regression in order to calculate the coefficients   and   of the regression line using the standard formulas (see, e.g., [32] ). Values   and   can be treated as statistics-based estimations for parameters  and  from relationships (11). 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 reliability of the method can be checked by calculating the correlation coefficients r i (see e.g., [13] ) for every epidemic wave and checking how close are their values is to unity. We can use also the F-test [13] for the null hypothesis that says that the proposed linear relationship (11) fits the data set. Similar approach was used in [7-11, 15, 16, 23-30, 33, 34] . To calculate the optimal values of parameters , , , , , we have to find the maximum of the correlation coefficient for the linear dependence (11) . The exact solution (7)-(9) allows avoiding numerical solutions of differential equations (1)-(3) and significantly reduces the time spent on calculations. A new algorithm [11, 29, 30] allows estimating the optimal values of SIR parameters for the i-th epidemic wave directly (without simulations of the previous waves). To reduce the number of unknown parameters, we can use the relationship (6) and (10). To estimate the value i V , we can use the smoothed accumulated number of cases [11, [26] [27] [28] [29] [30] 3 3 1 7 can be obtained with the use of (5) and formula (following from (2) and (3)). To estimate the average number of new cases dV/dt at the moment of time * i t in eq. (14), we can use the numerical differentiation of (13): and relationship (10). Thus we have only three independent parameters i  , i N and i  . To calculate the value of parameter i  , some iterations can be used (see details in [11] ). The optimal values of parameters and other characteristics of the ninth COVID-19 pandemic wave in Ukraine are listed in Table 1 we assumed that the numbers of registered cases coincide with the real one ( 9  =1). A similar SIR simulation of the 9th epidemic wave in Ukraine has already been reported in [30] , but now we have managed to find a new (larger in value) maximum of the correlation coefficient. The last column of Table 1 illustrate the results of SIR simulations with the non-prescribed value of 9  . The maximum of the correlation coefficient was achieved at 9  =4.1024. This result testifies that the main part of the epidemic in Ukraine is invisible. At the end of 2020 the real numbers of COVID-19 cases probably were more than 4 times higher than registered ones. The real final size of the ninth epidemic wave 9 V  is expected to be around 6 million. Unfortunately, we cannot wait for the end of the pandemic before the summer of 2022 (if vaccinations will not change this sad trend). Knowing the optimal values of parameters, the corresponding SIR curves can be easily calculated with the use of exact solution (7)  =1 (assuming that all the cases are registered). The red "circles", "triangles", and "stars" correspond to the accumulated numbers of cases registered during period of time taken for SIR simulations T c , before T c , and after T c , respectively (taken from Table A 100 . According to the results of our study, we can only say that in the case of suitability of the generalized SIR model, the value 9  =4.1024 and other optimal values of its parameters (given in the last column of Table 1 ) are the most reliable (provide the maximum value of the correlation coefficient). Therefore, we used additional methods to verify the calculations and showed some results perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in . According to the WHO report at the end of October, the number of detected cases in Slovakia was also approximately 1% of population [1] . Red markers show accumulated numbers of cases V j from Table A . "Circles" correspond to the accumulated numbers of cases taken for calculations (during period of time T c ); "triangles" -numbers of cases before T c ; "stars" -number of cases after T c . Blue and black colors correspond to the case 9  =4.1024; the blue "crosses" show derivative (16) Many authors are and will be trying to predict the COVID-19 pandemic dynamics in many countries and regions [7-11, 16, 23-30, 37-102] . The results of this study indicate that reliable estimates of its dynamics require consideration of incomplete data and constant changes of the conditions (quarantine restrictions, social distancing, coronavirus mutations, etc.) . 27 1206412 27 1347849 --28 1037362 28 1211593 28 1352134 --29 1045348 29 1216278 ----30 1055047 30 1219455 ----31 1064479 31 1221485 ---- perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in Coronavirus disease (COVID-2019) situation reports Clinical and virological data of the first cases of COVID-19 in Europe: a case series Estimating the early death toll of COVID-19 in the United States Long-term predictions for COVID-19 pandemic dynamics in Ukraine, Austria and Italy SIR-simulation of Corona pandemic dynamics in Europe Simulations and predictions of COVID-19 pandemic with the use of SIR model Hidden periods, duration and final size of COVID-19 pandemic COVID19 pandemic dynamics A Contribution to the mathematical theory of epidemics Mathematical Biology I/II Comparison of mathematical models for the dynamics of the Chernivtsi children disease Statistics based models for the dynamics of Chernivtsi children disease Statistics-based predictions of coronavirus epidemic spreading in mainland China Comparison of the coronavirus pandemic dynamics in Ukraine and neighboring countries Corona pandemic global stabilization? GLOBAL STABILIZATION TRENDS OF COVID-19 PANDEMIC Як довго українці сидітимуть на карантині? How long will the Ukrainians stay in quarantine? Динаміка COVID-19 епідемії в Україні та Києві після покращання тестування. COVID-19 epidemic dynamics in Ukraine and Kyiv after testing has improved Статистика пандемії COVID-19 в Україні та світі COVID-19 pandemic statistics in Ukraine and world Coronasummer in Ukraine and Austria Waves of COVID-19 pandemic. Detection and SIR simulations New waves of COVID-19 pandemic in Ukraine. (In Ukrainian) COVID-19 pandemic dynamics in Ukraine after Estimates of the COVID-19 pandemic dynamics in Ukraine based on two data sets Applied regression analysis Scaling macroscopic aquatic locomotion Maximal speed of underwater locomotion Nowcasting and Forecasting the Potential Domestic and International Spread of the 2019-nCoV Outbreak Originating in Wuhan, China: A Modelling Study Daozhou Gao, and others. Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak Eco-epidemiological assessment of the COVID-19 epidemic in China An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov) The reproductive number of COVID-19 is higher compared to SARS coronavirus Early dynamics of transmission and control of COVID-19: a mathematical modelling study Estimation of the final size of the COVID-19 epidemic Inferring COVID-19 spreading rates and potential change points for case number forecasts A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification Epidemic analysis of COVID-19 in China by dynamical modeling Modelling transmission and control of the COVID-19 pandemic in Australia Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 out break in mainland China An epidemiological forecast model and software assessing interventions on COVID-19 epidemic in China The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak Modeling the Declared New Cases of COVID-19 Trend Using Advanced Statistical Approaches Modelling transmission and control of the COVID-19 pandemic in Australia The reproductive index from SEIR model of Covid-19 epidemic in Asean Forecasting Covid-19 Dynamics in Brazil: A Data Driven Approach The reproduction number of COVID-19 and its correlation with public health interventions Forecasting Covid-19 Outbreak Progression in Italian Regions: A model based on neural network training from Chinese data Worldwide COVID-19 Outbreak Data Analysis and Prediction Analysis and forecast of COVID-19 spreading in China, Italy and France A model to predict COVID-19 epidemics with applications to South Korea Modeling and forecasting the early evolution of the Covid-19 pandemic in Brazil Dynamics of COVID-19 epidemics: SEIR models underestimate peak infection rates and overestimate epidemic duration Monitoring Italian COVID-19 spread by an adaptive SEIRD model A Contribution to the Mathematical Modeling of the Corona/COVID-19 Pandemic Covid-19 Outbreak Progression in Italian Regions: Approaching the Peak by the End of March in Northern Italy and First Week of April in Southern Italy Effects of social distancing and isolation on epidemic spreading: A dynamical density functional theory model Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions Why is it difficult to accurately predict the COVID-19 epidemic? Qualitative analysis of a stochastic SEITR epidemic model with multiple stages of infection and treatment Healthcare impact of COVID-19 epidemic in India: A stochastic mathematical model Mathematical prediction of the time evolution of the COVID-19 pandemic in Italy by a Gauss error function and Monte Carlo simulations Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China COVID-19: Development of a robust mathematical model and simulation package with consideration for ageing population and time delay for control action and resusceptibility Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China A mathematical model for COVID-19 transmission by using the Caputo fractional derivative Rabecca Tembo, Victor Daka. The COVID-19 Pandemic in Africa: Predictions using the SIR Model Investigation on the temporal evolution of the covid'19pandemic: prediction for Togo. Open Jornal of mathematical sciencies COVID-19 Pandemic Prediction for Hungary Time Dynamics of COVID-19. medRxiv 2020.05.21 Memory-Dependent Model for the Dynamics of COVID-19 Pandemic Evolution of COVID-19 Pandemic in India Mathematical Modeling of COVID-19 Pandemic in the African Continent Nowcasting the COVID-19 Pandemic in Bavaria COVID-19 Transmission Dynamics and Effectiveness of Public Health Interventions in New York City during the 2020 Spring Pandemic Wave A SEIR-like model with a time-dependent contagion factor describes the dynamics of the Covid-19 pandemic Ummay Soumayia Islam, Marjia Sultana. Forecasting the spread of COVID-19 pandemic in Bangladesh using ARIMA model A novel predictive mathematical model for COVID-19 pandemic with quarantine, contagion dynamics, and environmentally mediated transmission Modeling the Effective Control Strategy for Transmission Dynamics of Global Pandemic Forecasting COVID-19 pandemic Severity in Asia Adaptive COVID-19 Forecasting via Bayesian Optimization Romain Glele Kakai. Modeling COVID-19 dynamics in the sixteen West African countries Universal properties of the dynamics of the Covid-19 pandemics COVID-19 TRANSMISSION DYNAMICS IN INDIA WITH EXTENDED SEIR MODEL The amplified second outbreaks of global COVID-19 pandemic Analysis of Covid-19 Data for Eight European Countries and the United Kingdom Using a Simplified SIR Model Modeling, Control, and Prediction of the Spread of COVID-19 Using Compartmental, Logistic, and Gauss Models: A Case Study in Iraq and Egypt Comparison of ARIMA, ETS, NNAR and hybrid models to forecast the second wave of COVID-19 hospitalizations in Italy SIRSi compartmental model for COVID-19 pandemic with immunity loss Epidemic Analysis of COVID-19 in Egypt, Qatar and Saudi Arabia using the Generalized SEIR Model SEIRD MODEL FOR QATAR COVID-19 OUTBREAK: A CASE STUDY -16 931751 16 1160682 16 1280904 --17 944381 17 1163716 17 1287141 --18 956123 18 1167655 18 1293672 --19 964448 19 1172038 19 1299967 --20 970993 20 1177621 20 1304456 --21 979506 21 1182969 21 1307662 --22 989642 22 1187897 22 1311844 --23 1001132 23 1191812 23 1317694 --24 1012167 24 1194328 24 1325841 --25 1019876 25 1197107 25 1333844 --26 1025989 26 1200883 26 1342016 --27 1030374