Visible and Real Sizes of New COVID-19 Pandemic Waves in Ukraine

Authors

DOI:

https://doi.org/10.20535/ibb.2021.5.2.230487

Keywords:

COVID-19 pandemic, epidemic dynamics in Ukraine, mathematical modeling of infection diseases, SIR model, Parameter identification, statistical methods

Abstract

Background. To simulate the COVID-19 pandemic dynamics, various data sets and different mathematical models can be used. In particular, previous simulations for Ukraine were based on smoothing of the dependence of the number of cases on time, classical and the generalized SIR (susceptible-infected-removed) models. Different simulation and comparison methods were based on official accumulated number of laboratory confirmed cases and the data reported by Johns Hopkins University. Since both datasets are incomplete (a very large percentage of infected persons are asymptomatic), the accuracy of calculations and predictions is limited. In this paper we will try to assess the degree of data incompleteness and correct the relevant forecasts.

Objective. We aimed to estimate the real sizes of two new epidemic waves in Ukraine and compare them with visible dynamics based on the official number of laboratory confirmed cases. We also aimed to estimate the epidemic durations and final numbers of cases.

Methods. In this study we use the generalized SIR model for the epidemic dynamics and its known exact solution. The known statistical approach is adopted in order to identify both the degree of data incompleteness and parameters of SIR model.

Results. We have improved the method of estimating the unknown parameters of the generalized SIR model and calculated the optimal values ​​of the parameters. In particular, the visibility coefficients and the optimal values of the model parameters were estimated for two pandemic waves in Ukraine occurred in December 2020–March 2021. The real number of cases and the real number of patients spreading the infection versus time were calculated. Predictions of the real final sizes and durations of the pandemic in Ukraine are presented. If current trends continue, the end of the pandemic should be expected no earlier than in August 2022.

Conclusions. New method of the unknown parameters identification for the generalized SIR model was proposed, which allows estimating the coefficients of data incompleteness as well. Its application for two pandemic waves in Ukraine has demonstrated that the real number of COVID-19 cases is approximately four times higher than those shown in official statistics. Probably, this situation is typical for other countries. The reassessments of the COVID-19 pandemic dynamics in other countries and clarification of world forecasts are necessary.

References

Coronavirus Disease (COVID-19) Situation Reports [Internet]. Who.int. 2021 [cited 2021 Apr 6]. Available from: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports/

Li Q, Guan X, Wu P, Wang X, Zho L, Tong Y, et al. Early transmission dynamics in Wuhan, China, of novel coronavirus–infected pneumonia. New Engl J Med. 2020;382:1199-207. DOI: 10.1056/NEJMoa2001316

Italian doctors saw ‘strange pneumonia’ in Lombardy in November [Internet]. South China Morning Post. 2021 [cited 2021 Apr 6]. Available from: https://www.scmp.com/news/china/society/article/3076334/coronavirus-strange-pneumonia-seen-lombardy-november-leading

Lescure F, Bouadma L, Nguyen D, Parisey M, Wicky P, Behillil S, et al. Clinical and virological data of the first cases of COVID-19 in Europe: a case series. Lancet Infect Dis. 2020;20(6):697-706. DOI: 10.1016/S1473-3099(20)30200-0

Militärweltspiele in Wuhan: „Wir sind alle erkrankt“ [Internet]. FAZ.NET. 2021 [cited 2021 Apr 6]. Available from: https://m.faz.net/aktuell/sport/mehr-sport/militaerweltspiele-2019-in-wuhan-damals-schon-corona-faelle-16758894.html

Weinberger DM, Cohen T, Crawford FW, Mostashari F, Olson D, Pitzer VE, et al. Estimating the early death toll of COVID-19 in the United States. medRxiv [Preprint] 2020. DOI: 10.1101/2020.04.15.20066431

Nesteruk I. Simulations and predictions of COVID-19 pandemic with the use of SIR model. Innov Biosyst Bioeng. 2020;4(2):110-21. DOI: 10.20535/ibb.2020.4.2.204274

Nesteruk I. COVID-19 pandemic dynamics. Singapore: Springer; 2021. DOI: 10.1007/978-981-33-6416-5

Kermack WO, McKendrick AG. A Contribution to the mathematical theory of epidemics. J Royal Stat Soc Ser A. 1927;115:700-21.

Murray JD. Mathematical biology I/II. New York: Springer; 2002.

Langemann D, Nesteruk I, Prestin J. Comparison of mathematical models for the dynamics of the Chernivtsi children disease. Math Comp Simul. 2016;123:68-79. DOI: 10.1016/j.matcom.2016.01.003

Nesteruk I. Statistics based models for the dynamics of Chernivtsi children disease. Naukovi Visti NTUU KPI. 2017;5:26-34. DOI: 10.20535/1810-0546.2017.5.108577

Nesteruk I. Statistics-based predictions of coronavirus epidemic spreading in mainland China. Innov Biosyst Bioeng. 2020;4(1):13-8. DOI: 10.20535/ibb.2020.4.1.195074

Coronavirus in Ukraine - Statistics [15.03.2021] - Map of infections, graphs [Internet]. Index.minfin.com.ua. 2021 [cited 2021 Apr 6]. Available from: https://index.minfin.com.ua/ua/reference/coronavirus/ukraine/

Cabinet of Ministers of Ukraine – Home [Internet]. Kmu.gov.ua. 2021 [cited 2021 Apr 6]. Available from: https://www.kmu.gov.ua/

COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University [Internet]. GitHub. 2021 [cited 2021 Apr 6]. Available from: https://github.com/owid/covid-19-data/tree/master/public/data

Nesteruk I, Kydybyn I, Demelmair G. Global stabilization trends of COVID-19 pandemic. KPI Sci News. 2020;2:55-62. DOI: 10.20535/kpi-sn.2020.2.205124

Nesteruk I. Dynamics of the coronavirus pandemic in Italy and some global predictions. J Allergy Infect Dis. 2020;1(1):5-8.

Nesteruk I, Benlagha N. Predictions of COVID-19 pandemic dynamics in Ukraine and Qatar based on generalized SIR model. Innov Biosyst Bioeng. 2021;5(1):37-46. DOI: 10.20535/ibb.2021.5.1.228605

An experiment with mass testing for COVID-19 was conducted in Khmelnytsky| Podillya News [Internet]. Podillya News | News of Khmelnytsky region. 2021 [cited 2021 Mar 4]. Available from: https://podillyanews.com/2020/12/17/u-shkolah-hmelnytskogo-provely-eksperyment-z-testuvannyam-na-covid-19

Nesteruk I. General SIR model and its exact solution. In: COVID-19 pandemic dynamics. Singapore: Springer; 2021. DOI: 10.1007/978-981-33-6416-5_9

Nesteruk I. Comparison of the first waves of the COVID-19 pandemic in different countries and regions. In: COVID-19 Pandemic Dynamics. Singapore: Springer; 2021. DOI: 10.1007/978-981-33-6416-5_7

Draper NR, Smith H. Applied regression analysis. 3rd ed. John Wiley; 1998.

Gazzola M, Argentina M, Mahadevan L. Scaling macroscopic aquatic locomotion. Nature Physics. 2014;10:758-61. DOI: 10.1038/nphys3078

Nesteruk I. Maximal speed of underwater locomotion. Innov Biosyst Bioeng. 2019;3(3):152-67. DOI: 10.20535/ibb.2019.3.3.177976

Nesteruk I. Procedures of parameter identification for the waves of epidemics. In: COVID-19 pandemic dynamics. Singapore: Springer; 2021. DOI: 10.1007/978-981-33-6416-5_10

Slovakia tested most of the country in two days. Here's how they did it and what they found [Internet]. CNN. 2021 [cited 2021 Apr 6]. Available from: https://edition.cnn.com/2020/11/02/europe/slovakia-mass-coronavirus-test-intl/index.html

Slovakia's Second Round of Coronavirus Tests Draws Large Crowds [Internet]. Voice of America. 2021 [cited 2021 Apr 6]. Available from: https://www.voanews.com/covid-19-pandemic/slovakias-second-round-coronavirus-tests-draws-large-crowds

Nesteruk I. Classical SIR model and the exact solution of differential equations. In: COVID-19 pandemic dynamics. Singapore: Springer; 2021. DOI: 10.1007/978-981-33-6416-5_4

Wu JT , Leung K , Leung GM. Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: A modelling study. Lancet. 2020;395(10225):689-97. DOI: 10.1016/S0140-6736(20)30260-9

Zhao S, Lin Q, Ran J, Musa SS, Yang G, Wang W, et al. 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. Int J Infect Dis. 2020 Mar;92:214-7. DOI: 10.1016/j.ijid.2020.01.050

Byass P. Eco-epidemiological assessment of the COVID-19 epidemic in China, January–February 2020. Glob Health Action. 2020;13(1):1760490. DOI: 10.1080/16549716.2020.1760490

Tang B, Bragazzi NL, Li Q, Tang S, Xiao Y, Wu J. An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov). Infect Dis Model. 2020;5:248-55. DOI: 10.1016/j.idm.2020.02.001

Ying L, Gayle AA, Wilder-Smith A, Rocklöv J. The reproductive number of COVID-19 is higher compared to SARS coronavirus. J Travel Med. 2020;27(2):taaa021. DOI: https://doi.org/10.1093/jtm/taaa021

Kucharski AJ, Russell TW, Diamond C, Liu Y, Edmunds J, Funk S, et al. Early dynamics of transmission and control of COVID-19: a mathematical modelling study. Lancet Infect Dis. 2020 May;20(5):553-8. DOI: 10.1016/S1473-3099(20)30144-4

Batista M. Estimation of the final size of the COVID-19 epidemic. medRxiv [Preprint] 2020. DOI: 10.1101/2020.02.16.20023606

Dehning J, Zierenberg J, Spitzner FP, Wibral M, Pinheiro Neto J, Wilczek M, et al. Inferring COVID-19 spreading rates and potential change points for case number forecasts. arXiv [Preprint] 2020. arXiv:2004.01105

Chen Y, Cheng J, Jiang Y, Liu K. A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification. arXiv [Preprint] 2020. arXiv:2002.00418

Peng L, Yang W, Zhang D, Zhuge C, Hong L. Epidemic analysis of COVID-19 in China by dynamical modeling. medRxiv [Preprint] 2020. DOI: 10.1101/2020.02.16.20023465

Chang SL, Harding N, Zachreson C, Cliff OM, Prokopenko M. Modelling transmission and control of the COVID-19 pandemic in Australia. Nat Commun. 2020;11:5710. DOI: 10.1038/s41467-020-19393-6

Maier BF, Brockmann D. Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 out break in mainland China. Science. 2020;368(6492):742-6. DOI: 10.1126/science.abb4557

Wang L, Zhou Y, He J, Zhu B, Wang F, Tang L, et al. An epidemiological forecast model and software assessing interventions on the COVID-19 epidemic in China. Journal of Data Science. 2021;18(13):409-32. DOI: 10.6339/JDS.202007_18(3).0003

Chinazzi M, Davis JT, Ajelli M, Gioannini C, Litvinova M, Merler S, et al. The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak. Science. 2020;368(6489):395-400. DOI: 10.1126/science.aba9757

Zhang Y, Jiang B,Yuan J, Tao Y. The impact of social distancing and epicenter lockdown on the COVID-19 epidemic in mainland China: A data-driven SEIQR model study. medRxiv [Preprint] 2020. DOI: 10.1101/2020.03.04.20031187

Ghanam R, Boone EL, Abdel-Salam ASG. SEIRD model for Qatar Covid-19 outbreak: A case study. Lett Biomath. 2021;8(1):19-28.

Udomsamuthirun P, Chanilkul G, Tongkhonburi P, Meesubthong C. The reproductive index from SEIR model of Covid-19 epidemic in Asean. medRxiv [Preprint] 2020. DOI: 10.1101/2020.04.24.20078287

Pereira IG, Guerin JM, Silva Júnior AG, Garcia GS, Piscitelli P, Miani A, et al. Forecasting Covid-19 dynamics in brazil: A data driven approach. Int J Environ Res Public Health. 2020 Jul 15;17(14):5115. DOI: 10.3390/ijerph17145115

Linka K, Peirlinck M, Kuhl E. The reproduction number of COVID-19 and its correlation with public health interventions. Comput Mech. 2020;1-16. DOI: 10.1007/s00466-020-01880-8

Distante C, Gadelha Pereira I, Garcia Goncalves LM, Piscitelli P, Miani A. Forecasting Covid-19 outbreak progression in Italian regions: A model based on neural network training from Chinese data. medRxiv [Preprint] 2020. DOI: 10.1101/2020.04.09.20059055

Hamzah F, Binti A, Lau C, Nazri H, Ligot DV, Lee G, Tan CL. CoronaTracker: Worldwide COVID-19 outbreak data analysis and prediction. Bull World Health Organ. 2020. DOI: 10.2471/BLT.20.255695

Fanelli D, Piazza F. Analysis and forecast of COVID-19 spreading in China, Italy and France. Chaos Solitons Fractals. 2020;134:109761. DOI: 10.1016/j.chaos.2020.109761

Liu Z, Magal P, Seydi O, Webb GF. A model to predict COVID-19 epidemics with applications to South Korea, Italy, and Spain. medRxiv [Preprint] 2020. DOI: 10.1101/2020.04.07.20056945

Bastos SB, Cajueiro DO. Modeling and forecasting the early evolution of the Covid-19 pandemic in Brazil. Sci Rep. 2020;10:19457. DOI: 10.1038/s41598-020-76257-1

Grant A. Dynamics of COVID-19 epidemics: SEIR models underestimate peak infection rates and overestimate epidemic duration. medRxiv [Preprint] 2020. DOI: 10.1101/2020.04.02.20050674

Piccolomiini E L, Zama F. Monitoring Italian COVID-19 spread by an adaptive SEIRD model. medRxiv [Preprint] 2020. DOI: 10.1101/2020.04.03.20049734

Bärwolff G. A Contribution to the mathematical modeling of the Corona/COVID-19 pandemic. medRxiv [Preprint] 2020. DOI: 10.1101/2020.04.01.20050229

Distante C, Piscitelli P, Miani A. 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. Int J Environ Res Public Health. 2020 Apr 27;17(9):3025. DOI: 10.3390/ijerph17093025

te Vrugt M, Bickmann J, Wittkowski R. Effects of social distancing and isolation on epidemic spreading: A dynamical density functional theory model. Nat Commun. 2020;11:5576. DOI: 10.1038/s41467-020-19024-0

Yang Z, Zeng Z, Wang K, Wong SS, Liang W, Zanin M, et al. Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions. J Thorac Dis. 2020 Mar;12(3):165-74. DOI: 10.21037/jtd.2020.02.64

Roda WC, Varughese MB, Han D, Li MY. Why is it difficult to accurately predict the COVID-19 epidemic? Infect Dis Model. 2020;5:271-81. DOI: 10.1016/j.idm.2020.03.001

Otunuga OM, Ogunsolu MO. Qualitative analysis of a stochastic SEITR epidemic model with multiple stages of infection and treatment. Infect Dis Model. 2019 Dec 14;5:61-90. DOI: 10.1016/j.idm.2019.12.003

Chatterjee K, Chatterjee K, Kumar A, Shankard S. Healthcare impact of COVID-19 epidemic in India: A stochastic mathematical model. Med J Armed Forces India. 2020;76(2):147-55. DOI: 10.1016/j.mjafi.2020.03.022

Ciufolini I, Paolozzi A. Mathematical prediction of the time evolution of the COVID-19 pandemic in Italy by a Gauss error function and Monte Carlo simulations. Eur Phys J Plus. 2020;135:355. DOI: 10.1140/epjp/s13360-020-00383-y

Annas S, Isbar Pratama M, Rifandi M, Sanusi W, Side S. Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia. Chaos Solitons Fractals. 2020;139:110072. DOI: 10.1016/j.chaos.2020.110072

Yadav RP, Verma R. A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China. Chaos Solitons Fractals. 2020;140:110124. DOI: 10.1016/j.chaos.2020.110124

Ng KY, Gui MM. COVID-19: Development of a robust mathematical model and simulation package with conside¬ration for ageing population and time delay for control action and resusceptibility. Physica D. 2020 Oct;411:132599. DOI: 10.1016/j.physd.2020.132599

Ivorra B, Ferrández MR, Vela-Pérez M, Ramos AM. Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China. Commun Nonlinear Sci Numer Simul. 2020;88:105303. DOI: 10.1016/j.cnsns.2020.105303

Tuan NH, Mohammadi H, Rezapour S. A mathematical model for COVID-19 transmission by using the Caputo fractional derivative. Chaos Solitons Fractals. 2020;140:110107. DOI: 10.1016/j.chaos.2020.110107

Sinkala M, Nkhoma P, Zulu M, Kafita D, Tembo R, Daka V. The COVID-19 pandemic in Africa: Predictions using the SIR model. medRxiv [Preprint] 2020. DOI: 10.1101/2020.06.01.20118893

Agbokou K, Gneyou K, Tcharie K. Investigation on the temporal evolution of the covid'19pandemic: prediction for Togo. Open J Math Sci. 2020;4:273-9. DOI: 10.30538/oms2020.0118

Pintér G, Felde I, Mosavi A, Gloaguen R. COVID-19 Pandemic prediction for Hungary; A hybrid machine learning approach. Mathematics. 2020;8:890. DOI: 10.3390/math8060890

Rossman H, Shilo S, Meir T, Gorfine M, Shalit U, Segal E. Patterns of COVID-19 pandemic dynamics following deployment of a broad national immunization program. medRxiv [Preprint] 2021. DOI: 10.1101/2021.02.08.21251325

Furati KM, Sarumi IO, Khaliq AQM. Memory-dependent model for the dynamics of COVID-19 pandemic. medRxiv [Preprint] 2020. DOI: 10.1101/2020.06.26.20141242

Bosch J, Wilson A, O'Neil K, Zimmerman PA. COVID-19 predict - predicting pandemic trends. medRxiv [Preprint] 2020. DOI: 10.1101/2020.09.09.20191593

Asad A, Srivastava S, Verma MK. Evolution of COVID-19 pandemic in India. Trans Indian Natl Acad Eng. 2020 Sep; 1-8. DOI: 10.1007/s41403-020-00166-y

Aries N, Ounis H. Mathematical modeling of COVID-19 pandemic in the African continent. medRxiv [Preprint] 2020. DOI: 10.1101/2020.10.10.20210427

Günther F, Bender A, Katz K, Kuechenhoff H, Hoehle M. Nowcasting the COVID-19 pandemic in Bavaria. Biom J. 2020 Dec. DOI: 10.1002/bimj.202000112

Yang W, Shaff J, Shaman J. COVID-19 Transmission dynamics and effectiveness of public health interventions in New York City during the 2020 Spring pandemic wave. medRxiv [Preprint] 2020. DOI: 10.1101/2020.09.08.20190710

Dickman R. A SEIR-like model with a time-dependent contagion factor describes the dynamics of the Covid-19 pandemic. medRxiv [Preprint] 2020. DOI: 10.1101/2020.08.06.20169557

Kundu LR, Ferdous MZ, Islam US, Sultana M. Forecasting the spread of COVID-19 pandemic in Bangladesh using ARIMA model. medRxiv [Preprint] 2020. DOI: 10.1101/2020.10.22.20217414

Barbastefano R, Carvalho D, Lippi MC, Pastore D. A novel predictive mathematical model for COVID-19 pandemic with quarantine, contagion dynamics, and environmentally mediated transmission. medRxiv [Preprint] 2020. DOI: 10.1101/2020.07.27.20163063

Biswas MHA, Khatun MS, Paul AK, Khatun MR, Islam MA, Samad SA, et al. Modeling the effective control strategy for transmission dynamics of global pandemic COVID-19. medRxiv [Preprint] 2020. DOI: 10.1101/2020.04.22.20076158

Aviv-Sharon E, Aharoni A. Forecasting COVID-19 pandemic severity in Asia. medRxiv [Preprint] 2020. DOI: 10.1101/2020.05.15.20102640

Bannur N, Maheshwari H, Jain S, Shetty S, Merugu S, Raval A. Adaptive COVID-19 Forecasting via Bayesian Optimization. In: Proceedings of 8th ACM IKDD CODS and 26th COMAD; 2020. DOI: 10.1145/3430984.3431047

Honfo SH, Taboe BH, Kakaï RG. Modeling COVID-19 dynamics in the sixteen West African countries. medRxiv [Preprint] 2020. DOI: 10.1101/2020.09.04.20188532

Chruściel PT, Szybka SJ. Universal properties of the dynamics of the Covid-19 pandemics. medRxiv [Preprint] 2020. DOI: 10.1101/2020.08.24.20181214

Reddy BRM, Singh A, Srivastava P. Covid-19 transmission dynamics in India with extended SEIR model. medRxiv [Preprint] 2020. DOI: 10.1101/2020.08.15.20175703

Huang J, Liu X, Zhang L, Yang K, Chen Y, Huang Z, et al. The amplified second outbreaks of global COVID-19 pandemic. medRxiv [Preprint] 2020. DOI: 10.1101/2020.07.15.20154161

Bhanot G, DeLisi C. Analysis of Covid-19 data for eight European countries and the United Kingdom using a simplified SIR Model. medRxiv [Preprint] 2020. DOI: 10.1101/2020.05.26.20114058

Ibrahim MA, Al-Najafi A. Modeling, control, and prediction of the spread of Covid-19 using compartmental, logistic, and gauss models: A case study in Iraq and Egypt. Processes. 2020;8(11):1400. DOI: 10.3390/pr8111400

Perone G. Comparison of ARIMA, ETS, NNAR and hybrid models to forecast the second wave of COVID-19 hospitalizations in Italy. SSRN [Preprint] 2020. DOI: 10.2139/ssrn.3716343

Bueno AM, Batistela CM, Correa DPF, Piqueira JRC. SIRSi compartmental model for COVID-19 pandemic with immunity loss. Chaos Solitons Fractals. 2021 Jan;142:110388. DOI: 10.1016/j.chaos.2020.110388

Fahmya AE, El-desoukya MM, Mohamed ASA. Epidemic Analysis of COVID-19 in Egypt, Qatar and Saudi Arabia using the generalized SEIR model. medRxiv [Preprint] 2020. DOI: 10.1101/2020.08.19.20178129

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2021-08-12

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Nesteruk I. Visible and Real Sizes of New COVID-19 Pandemic Waves in Ukraine. Innov Biosyst Bioeng [Internet]. 2021Aug.12 [cited 2021Sep.20];5(2):85-96. Available from: http://ibb.kpi.ua/article/view/230487

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