DOI: https://doi.org/10.20535/ibb.2020.4.2.204274

Simulations and Predictions of COVID-19 Pandemic With the Use of SIR Model

Igor Nesteruk

Abstract


Background. The COVID-19 pandemic is of great interest to researchers due to high mortality and a very negative impact to the world economy. A detailed scientific analysis of the phenomenon is yet to come, but the public is already interested in the problems of duration of the epidemic, the expected number of patients, where and when the pandemic started. Correct simulation of the pandemic dynamics needs complicated mathematical models and many efforts for unknown parameters identification. In this article, preliminary estimates for many countries and world will be presented, summarized and discussed.

Objective. We will estimate the epidemic characteristics for USA, Germany, UK, the Republic of Korea and in the world with the use of SIR simulations and compare them with the results obtained before for Italy, Spain, France, the Republic of Moldova, Ukraine and Kyiv. The hidden periods, epidemic durations, final numbers of cases and quarantine measures will be discussed.

Methods. In this study we use the known SIR (susceptible-infected-removed) model for the dynamics of the epidemic, the known exact solution of the linear differential equations and statistical approach developed before.

Results. The optimal values of the SIR model parameters were identified with the use of statistical approach for epidemic dynamics in USA, Germany, UK, the Republic of Korea, and in the world. The actual number of cases and the number of patients spreading the infection versus time were calculated. The hidden periods, durations and final sizes of the epidemic were evaluated. In particular, the pandemic began in China no later than October, 2019. If current trends continue, the end of the pandemic should be expected no earlier than March 2021, the global number of cases will exceed 5 million. A simple method for assessing the risk of premature weakening of quarantines is proposed.

Conclusions. The SIR model and statistical approach to the parameter identification are helpful to make some reliable estimations for the epidemic dynamics, e.g., the real time of the outbreak, final size and duration of the epidemic and the number of persons spreading the infection versus time. This information will be useful to regulate the quarantine activities and to predict the medical and economic consequences of the pandemic.


Keywords


Coronavirus pandemic; Epidemic outbreak; Coronavirus COVID-19; Mathematical modeling of infection diseases; SIR model; Parameter identification; Statistical methods

Full Text:

PDF

References


Coronavirus Disease (COVID-19) Situation Reports [Internet]. Who.int. 2020 [cited 2020 May 9]. Available from: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports/

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.

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

Nesteruk I. Characteristics of coronavirus epidemic in mainland China estimated with the use of official data available after February 12, 2020. ResearchGate [Preprint] 2020. DOI: 10.13140/RG.2.2.19667.32804

Nesteruk I. Estimations of the coronavirus epidemic dynamics in South Korea with the use of SIR model. ResearchGate [Preprint] 2020. DOI: 10.13140/RG.2.2.15489.40807

Nesteruk I. Comparison of the coronavirus epidemic dynamics in Italy and mainland China MEDRXIV [Preprint] 2020. Available from: https://medrxiv.org/cgi/content/short/2020.03.18.20038133v1

Nesteruk I. Stabilization of the coronavirus pandemic in Italy and global prospects. MEDRXIV [Preprint] 2020. DOI: 10.1101/2020.03.28.20045898

Nesteruk I. Long-term predictions for COVID-19 pandemic dynamics in Ukraine, Austria and Italy. MEDRXIV [Preprint] 2020. DOI: 10.1101/2020.04.08.20058123

Nesteruk I. SIR-simulation of Corona pandemic dynamics in Europe. MEDRXIV [Preprint] 2020. DOI: 10.1101/2020.04.22.20075135

Nesteruk I. COVID-19 epidemic dynamics in Ukraine and Kyiv after testing has improved. ResearchGate [Preprint] 2020. DOI: 10.13140/RG.2.2.36705.86885

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

Statistical tables [Internet]. Onlinepubs.trb.org. 2020 [cited 2020 May 9]. Available from: https://onlinepubs.trb.org/onlinepubs/nchrp/cd-22/manual/v2appendixc.pdf

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

Italian doctors saw ‘strange pneumonia’ in Lombardy in November [Internet]. South China Morning Post. 2020 [cited 2020 May 9]. Available from: https://www.scmp.com/news/china/society/article/3076334/coronavirus-strange-pneumonia-seen-lombardy-november-leading

GmbH F. Militärweltspiele in Wuhan: „Wir sind alle erkrankt“ [Internet]. FAZ.NET. 2020 [cited 2020 May 9]. 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 F, 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

Trump 'considering quarantining New York' [Internet]. BBC News. 2020 [cited 2020 May 9]. Available from: https://www.bbc.com/news/world-us-canada-52079121

Hong Kong takes emergency steps as mystery ‘pneumonia’ infects 27 in Wuhan [Internet]. South China Morning Post. 2020 [cited 2020 May 9]. Available from: https://www.scmp.com/news/china/politics/article/3044050/mystery-illness-hits-chinas-wuhan-city-nearly-30-hospitalised


GOST Style Citations


 

 







Copyright (c) 2020 The Author(s)

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.