J Korean Med Sci.  2020 Apr;35(13):e143. 10.3346/jkms.2020.35.e143.

School Opening Delay Effect on Transmission Dynamics of Coronavirus Disease 2019 in Korea: Based on Mathematical Modeling and Simulation Study

• Kim S
• Kim YJ
• Peck KR
• Jung E

• KMID: 2509607
• DOI: http://doi.org/10.3346/jkms.2020.35.e143

Abstract

Background
Nonpharmaceutical intervention strategy is significantly important to mitigate the coronavirus disease 2019 (COVID-19) spread. One of the interventions implemented by the government is a school closure. The Ministry of Education decided to postpone the school opening from March 2 to April 6 to minimize epidemic size. We aimed to quantify the school closure effect on the COVID-19 epidemic.
Methods
The potential effects of school opening were measured using a mathematical model considering two age groups: children (aged 19 years and younger) and adults (aged over 19). Based on susceptible-exposed-infectious-recovered model, isolation and behavior-changed susceptible individuals are additionally considered. The transmission parameters were estimated from the laboratory confirmed data reported by the Korea Centers for Disease Control and Prevention from February 16 to March 22. The model was extended with estimated parameters and estimated the expected number of confirmed cases as the transmission rate increased after school opening.
Results
Assuming the transmission rate between children group would be increasing 10 fold after the schools open, approximately additional 60 cases are expected to occur from March 2 to March 9, and approximately additional 100 children cases are expected from March 9 to March 23. After March 23, the number of expected cases for children is 28.4 for 7 days and 33.6 for 14 days.
Conclusion
The simulation results show that the government could reduce at least 200 cases, with two announcements by the Ministry of education. After March 23, although the possibility of massive transmission in the children's age group is lower, group transmission is possible to occur.

Keyword

COVID-19; Mathematical Modeling; Behavior Changes; School Opening Delay; School Closures

Figure

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  Fig. 1 Flow diagram of coronavirus disease 2019 transmission dynamics.S = susceptible individuals, SF = behavior-changed susceptible individuals, E = exposed individuals, I = infectious individuals, Q = confirmed and isolated individuals, R = removed individuals.

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  Fig. 2 Best datafit results from February 16 to March 2. Circles indicate the daily reported confirmed data from Korea Centers for Disease Control and Prevention press and solid curves display the model curve using estimated parameters. (A) Children. (B) Adults.

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  Fig. 3 Expected number of confirmed cases from March 2 to March 9. (A) Children. (B) Adults.

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  Fig. 4 Best datafit results from February 16 to March 9. Circles indicate the daily reported confirmed data from Korea Centers for Disease Control and Prevention press and solid curves display the model curve using estimated parameters. (A) Children. (B) Adults.

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  Fig. 5 Expected number of confirmed cases from March 9 to March 23. (A) Children. (B) Adults.

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  Fig. 6 Best datafit results from February 16 to March 22 and its extension until March 23. Circles indicate the daily reported confirmed data from Korea Centers for Disease Control and Prevention press and solid curves display the model curve using estimated parameters. (A) Children. (B) Adults.

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  Fig. 7 Expected number of confirmed cases for 7 days after March 23. (A) Children. (B) Adults.

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  Fig. 8 Expected number of confirmed cases for 14 days after March 23. (A) Children. (B) Adults.

Reference

1. Korean Society of Infectious DiseasesKorean Society of Pediatric Infectious DiseasesKorean Society of EpidemiologyKorean Society for Antimicrobial TherapyKorean Society for Healthcare-associated Infection Control and PreventionKorea Centers for Disease Control and Prevention. Report on the Epidemiological features of coronavirus disease 2019 (COVID-19) outbreak in the Republic of Korea from January 19 to March 2, 2020. J Korean Med Sci. 2020; 35(10):e112. PMID: 32174069.

2. KCDC Press. Daily Cumulative Confirmed Data. Cheongju: Korea Centers for Disease Control and Prevention;2020.

3. Statistics Korea. Resident Registration Population by Administrative District and Age: Korean, Author's Translation. . Daejeon: Statistics Korea;2020.

4. Towers S, Feng Z. Pandemic H1N1 influenza: predicting the course of a pandemic and assessing the efficacy of the planned vaccination programme in the United States. Euro Surveill. 2009; 14(41):19358. PMID: 19883540.

5. Kim S, Lee J, Jung E. Mathematical model of transmission dynamics and optimal control strategies for 2009 A/H1N1 influenza in the Republic of Korea. J Theor Biol. 2017; 412:74–85. PMID: 27769686.

6. 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.

7. Fang Y, Nie Y, Penny M. Transmission dynamics of the COVID-19 outbreak and effectiveness of government interventions: as data-driven analysis. J Med Virol. 2020; jmv.25750.

8. Choi SC, Ki M. Estimating the reproductive number and the outbreak size of Novel Coronavirus disease (COVID-19) using mathematical model in Republic of Korea. Epidemiol Health. 2020; e2020011. PMID: 32164053.

9. Perra N, Balcan D, Gonçalves B, Vespignani A. Towards a characterization of behavior-disease models. PLoS One. 2011; 6(8):e23084. PMID: 21826228.

10. Korea Centers for Disease and Control. Korean Situation Report of COVID-19 on Feburary 16: Korean, Author's Translation. Cheongju: Korea Centers for Disease and Control;2020.

11. Ki M. Task Force for 2019-nCoV. Epidemiologic characteristics of early cases with 2019 novel coronavirus (2019-nCoV) disease in Korea. Epidemiol Health. 2020; 42:e2020007. PMID: 32035431.

12. KOrean Statistical information Service. Statistics of Kindergarten (2019-11-12). Daejeon: Statistic Korea;2019.

13. KOrean Statistical information Service. Statistics of Childcare by Age (2019-07-08). Daejeon: Statistics Korea;2019.

14. KOrean Statistical information Service. Statistics of Elementry School (2019-11-13). Daejeon: Statistics Korea;2019.

15. KOrean Statistical information Service. Statistics of Middle School (2019-11-13). Daejeon: Statistics Korea;2019.

16. KOrean Statistical information Service. Statistics of High School (2019-11-13). Daejeon: Statistics Korea;2019.

17. The MathWorks, Inc. MATLAB. https://kr.mathworks.com/products/matlab.html.

18. Wu JT, Leung K, Perera RA, Chu DK, Lee CK, Hung IF, et al. Inferring influenza infection attack rate from seroprevalence data. PLoS Pathog. 2014; 10(4):e1004054. PMID: 24699693.

19. Chu HY, Kuypers J, Renaud C, Wald A, Martin E, Fairchok M, et al. Molecular epidemiology of respiratory syncytial virus transmission in childcare. J Clin Virol. 2013; 57(4):343–350. PMID: 23684816.