Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Estimation of the Time Dependent Reproduction Number of Novel Coronavirus (COVID 19) for Turkey in the Late Stage of the Outbreak
Türkiye İçin Salgının Geç Evresinde Yeni Tip Koronavirüsün (COVID-19) Zamana Bağlı Bulaştırma Katsayısının Tahmini
Serdal Kenan KÖSEa, Emre DEMİRb, Gülçin AYDOĞDUb
aDepartment of Biostatistics, Ankara University Faculty of Medicine, Ankara, TURKEY
bDepartment of Biostatistics, Hitit University Faculty of Medicine, Çorum, TURKEY
Turkiye Klinikleri J Biostat. 2021;13(1):103-11
doi: 10.5336/biostatic.2020-79473
Article Language: EN
Full Text
ABSTRACT
Objective: Coronavirus disease-2019 (COVID-19), which caused a big outbreak, was first detected in Wuhan, China on 31st of December, 2019, and began to spread all over the world rapidly. The first case in Turkey was detected on the 11th of March, 2020. This study aims to calculate time-dependent (TD) reproduction number (Rt) using three different serial interval values in the late phase of the COVID-19 pandemic for Turkey. Material and Methods: TD model was used for estimation of reproduction number. For the serial interval of the coronavirus, the serial interval values of 4±2.5 and 6±3 days were used together with the severe acute respiratory syndrome and Middle East respiratory syndrome serial interval mean of 8±3.6. Gamma distribution was used for serial interval estimates. The bootstrap method with 1,000 simulations was used for all reproduction number confidence interval estimates. Results: Using 8±3.6, 6±3 and 4±2.5 serial interval values, the mean reproduction number (Rt) calculated for Turkey with the TD model was 2.06 (1.92-2.21), 1.70 (1.58-1.81), and 1.39 (1.30- 1.48), respectively. The confidence intervals of the reproduction number values calculated for Turkey range from 1.30 (lowest) to 2.21 (highest). Conclusion: According to the TD model results, from the first day when the pandemic started in Turkey to the 32nd (11th of April 2020) and 33rd (12th of April 2020) days, the Rt value decreased below 1 and the outbreak started to demonstrate a breaking point. Lower Rt in Turkey compared to the other epicenters of the world may indicate that Turkey was quicker in implementing preventive measures much earlier than the other countries.

Keywords: Coronavirus; COVID-19; reproduction number; outbreak; infectious disease; epidemiology; statistical modelling
ÖZET
Amaç: Büyük bir salgına neden olan koronavirüs hastalığı2019 [coronavirus disease-2019 (COVID-19)], ilk olarak 31 Aralık 2019'da Çin'in Wuhan şehrinde ortaya çıktı ve hızlı bir şekilde tüm dünyaya yayılmaya başladı. Türkiye'de ilk vaka 11 Mart 2020'de tespit edildi. Bu çalışma, Türkiye için COVID-19 salgınının geç evresinde 3 farklı seri aralık senaryosu kullanarak, zamana bağlı [time dependent (TD)] bulaştırma katsayısını (Rt) hesaplamayı amaçlamaktadır. Gereç ve Yöntemler: Bulaştırma katsayısının tahmini için TD model kullanılmıştır. Koronavirüsün seri aralığı için şiddetli akut solunum sendromu ve Orta Doğu solunum sendromu seri aralığı ortalaması (8±3,6 gün) ile birlikte 4±2,5 ve 6±3 günlük seri aralık değerleri kullanılmıştır. Seri aralık tahmini için Gamma dağılımı kullanılmıştır. Bulaştırma katsayılarının güven aralığı tahminleri için 1.000 benzetim ile Bootstrap yöntemi kullanılmıştır. Bulgular: TD modeli ile Türkiye için 8±3,6, 6±3 ve 4±2,5 seri aralık değerleri kullanılarak hesaplanan ortalama bulaştırma katsayıları (Rt) sırasıyla 2,06 (1,92-2,21), 1,70 (1,58- 1,81) ve 1,39 (1,30-1,48) olarak bulunmuştur. Türkiye için hesaplanan bulaştırma katsayısı güven aralıklarının 1,30 (en düşük) ile 2,21 (en yüksek) arasında değiştiği belirlenmiştir. Sonuç: TD modeli sonuçlarına göre Türkiye'de salgının başladığı ilk günden sonra 32 (11 Nisan 2020) ve 33. (12 Nisan 2020) günlerde Rt değerinin ilk kez 1'in altına düştüğü ve salgının kırılmaya başladığı belirlenmiştir. Rt değerinin diğer ülkelere göre daha düşük olmasında diğer birçok ülkeden önce alınan önlemlerin etkili olduğu düşünülmektedir.

Anahtar Kelimeler: Koronavirüs; COVID-19; bulaştırma katsayısı; salgın; bulaşıcı hastalık; epidemiyoloji; istatistiksel modelleme
REFERENCES:
  1. Lai A, Bergna A, Acciarri C, Galli M, Zehender G. Early phylogenetic estimate of the effective reproduction number of SARS-CoV-2. J Med Virol. 2020;92(6):675-9. [Crossref]  [PubMed]  [PMC] 
  2. Alimohamadi Y, Taghdir M, Sepandi M. Estimate of the basic reproduction number for covid-19: a systematic review and meta-analysis. J Prev Med Public Health. 2020;53(3):151-7. [Crossref]  [PubMed]  [PMC] 
  3. 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;92:214-7. [Crossref]  [PubMed]  [PMC] 
  4. Park SE. Epidemiology, virology, and clinical features of severe acute respiratory syndrome -coronavirus-2 (SARS-CoV-2; Coronavirus Disease-19). Clin Exp Pediatr. 2020;63(4):119-24. [Crossref]  [PubMed]  [PMC] 
  5. You C, Deng Y, Hu W, Sun J, Lin Q, Zhou F, et al. Estimation of the time-varying reproduction number of COVID-19 outbreak in China. Int J Hyg Environ Health. 2020;228:113555. [PubMed]  [PMC] 
  6. Sau A, Phadikar S, Bhakta I. Estimation of Time Dependent Reproduction Number for the Ongoing COVID-2019 Pandemic 2020. Available at SSRN 3556672. [Crossref] 
  7. Breban R, Vardavas R, Blower S. Theory versus data: how to calculate R0? PLoS One. 2007;2(3):e282. [Crossref]  [PubMed]  [PMC] 
  8. Zhou T, Liu Q, Yang Z, Liao J, Yang K, Bai W, et al. Preliminary prediction of the basic reproduction number of the Wuhan novel coronavirus 2019-nCoV. J Evid Based Med. 2020;13(1):3-7. [Crossref]  [PubMed]  [PMC] 
  9. Wang Y, You XY, Wang YJ, Peng LP, Du ZC, Gilmour S, et al. [Estimating the basic reproduction number of COVID-19 in Wuhan, China]. Zhonghua Liu Xing Bing Xue Za Zhi. 2020;41(4):476-9. [PubMed] 
  10. Zhang S, Diao M, Yu W, Pei L, Lin Z, Chen D. Estimation of the reproductive number of novel coronavirus (COVID-19) and the probable outbreak size on the Diamond Princess cruise ship: A data-driven analysis. Int J Infect Dis. 2020;93:201-4. [Crossref]  [PubMed]  [PMC] 
  11. Yuan J, Li M, Lv G, Lu ZK. Monitoring transmissibility and mortality of COVID-19 in Europe. Int J Infect Dis. 2020;95:311-5. [Crossref]  [PubMed]  [PMC] 
  12. D'Arienzo M, Coniglio A. Assessment of the SARS-CoV-2 basic reproduction number, R0, based on the early phase of COVID-19 outbreak in Italy. Biosaf Health. 2020;2(2):57-9. [Crossref]  [PubMed]  [PMC] 
  13. Flaxman S, Mishra S, Gandy A, Unwin HJT, Mellan TA, Coupland H, et al; Imperial College COVID-19 Response Team, Ghani AC, Donnelly CA, Riley S, Vollmer MAC, Ferguson NM, Okell LC, Bhatt S. Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe. Nature. 2020;584(7820):257-61. [Crossref]  [PubMed] 
  14. Deb S, Majumdar M. A time series method to analyze incidence pattern and estimate reproduction number of COVID-19. arXiv: 2003.10655v1 [stat.AP] 2020. [Link] 
  15. Obadia T, Haneef R, Boëlle PY. The R0 package: a toolbox to estimate reproduction numbers for epidemic outbreaks. BMC Med Inform Decis Mak. 2012;12:147. [Crossref]  [PubMed]  [PMC] 
  16. Wallinga J, Teunis P. Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. Am J Epidemiol. 2004;160(6):509-16. [Crossref]  [PubMed]  [PMC] 
  17. Counotte MJ, Kim CR, Wang J, Bernstein K, Deal CD, Broutet NJN, et al. Sexual transmission of Zika virus and other flaviviruses: A living systematic review. PLoS Med. 2018;15(7):e1002611. [Crossref]  [PubMed]  [PMC] 
  18. Arzt J, Branan MA, Delgado AH, Yadav S, Moreno-Torres KI, Tildesley MJ, et al. Quantitative impacts of incubation phase transmission of foot-and-mouth disease virus. Scientific Reports. 2019;9(1):1-13. [Link] 
  19. World Health Organization: Principles of infectious disease transmission. 2009 [Link]  (accession date: May 15, 2020)
  20. Nishiura H, Linton NM, Akhmetzhanov AR. Serial interval of novel coronavirus (COVID-19) infections. Int J Infect Dis. 2020;93:284-6. [Crossref]  [PubMed]  [PMC] 
  21. 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. N Engl J Med. 2020;382(13):1199-207. [PubMed]  [PMC] 
  22. Du Z, Xu X, Wu Y, Wang L, Cowling BJ, Meyers LA. The serial interval of COVID-19 from publicly reported confirmed cases. medRxiv [Preprint]. 2020:2020.02.19.20025452. Update in: Emerg Infect Dis. 2020;26(6):1341-3. [Crossref]  [PubMed]  [PMC] 
  23. Park M, Cook AR, Lim JT, Sun Y, Dickens BL. A systematic review of COVID-19 epidemiology based on current evidence. J Clin Med. 2020;9(4):967. [Crossref]  [PubMed]  [PMC] 
  24. Ridenhour B, Kowalik JM, David KS. Unraveling R0: Considerations for public health applications. American Journal of Public Health 2018;108(S6):S445-S454. [Crossref]  [PMC] 

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