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Volume 26, Number 11—November 2020
Online Report

Early Insights from Statistical and Mathematical Modeling of Key Epidemiologic Parameters of COVID-19

Matthew Biggerstaff, Benjamin J. Cowling, Zulma M. Cucunubá, Linh Dinh, Neil M. Ferguson, Huizhi Gao, Verity Hill, Natsuko Imai, Michael A. Johansson, Sarah Kada, Oliver Morgan, Ana Pastore y Piontti, Jonathan A. Polonsky, Pragati Venkata Prasad, Talia M. Quandelacy, Andrew Rambaut, Jordan W. Tappero, Katelijn A. VandemaeleComments to Author , Alessandro Vespignani, K. Lane Warmbrod, Jessica Y. Wong, and for the WHO COVID-19 Modelling Parameters Group
Author affiliations: Centers for Disease Control and Prevention, Atlanta, Georgia, USA (M. Biggerstaff, M.A. Johansson, S. Kada, P.V. Prasad, T.M. Quandelacy); University of Hong Kong, Hong Kong, China (B.J. Cowling, H. Gao, J.Y. Wong); Imperial College London, London, UK (Z.M. Cucunubá, N.M. Ferguson, N. Imai); World Health Organization, Geneva, Switzerland (L. Dinh, O. Morgan, J.A. Polonsky, J.W. Tappero, K.A. Vandemaele, K.L. Warmbrod); University of Edinburgh, Edinburgh, Scotland, UK (V. Hill, A. Rambaut); Northeastern University, Boston, Massachusetts, USA (A. Pastore y Piontti, A. Vespignani); ISI Foundation, Turin, Italy (A. Vespignani)

Main Article

Table 2

Summary of estimates of mean evolutionary rate and most recent common ancestor of COVID-19*

Mean evolutionary rate (95% CI) MRCA (95% CI) No. genomes analyzed Clock model† Growth model Source
2019 Nov 29
(Nov 8–Dec 16)
Rambaut, unpub. data,
1.23 × 10−3 (0.56 × 10−3 to 1.98 × 10−3)
2019 Nov 21 (Oct 23–Dec 13)
Duchene et al., unpub. data,
1.29 × 10−3 (0.535 × 10−4 to 2.15 × 10−3)
2019 Nov 14 (Sep 28–Dec 13)
Duchene et al., unpub. data,
0.9 × 10−3 (0.5 × 10−3 to 1.4 × 10−3)
2019 Dec 3 (Oct 30–Dec 17)
Bedford, unpub. data,
0.92 × 10−3 (0.33 × 10−3 to 1.46×10−3)
2019 Nov 29 (Oct 28–Dec 20)
Rambaut, unpub. data, Accessed March 4, 2020
1.04 × 10−3 (0.71 × 10−3 to 1. 4 ×10−3)
2019 Dec 3 (Nov 16–Dec 17)
Hill and Rambaut, unpub. data,
7.41×10−4 (4.91 × 10−4 to 1.02 × 10−3) 2019 Nov 27 (Nov 7–Dec 11) 128 Strict Birth–death model Sciré et al., unpub. data,

*MRCA, most recent common ancestor; NA, not applicable; UNCL, uncorrelated.
†The clock model is a technique that uses the mutation rate to estimate the time of emergence (48).

Main Article

  1. World Health Organization. Novel coronavirus (2019-nCoV) situation report 1. 2020 Jan [cited 2020 Mar 1].
  2. World Health Organization. Coronavirus disease 2019 (COVID-19) situation report 47. 2020 Mar [cited 2020 Mar 1].
  3. World Health Organization Health Emergencies Programme. Q&A on coronaviruses (COVID-19). 2020 [cited 2020 Feb 26].
  4. Wu  JT, Cowling  BJ. The use of mathematical models to inform influenza pandemic preparedness and response. Exp Biol Med (Maywood). 2011;236:95561. DOIPubMedGoogle Scholar
  5. Garske  T, Cori  A, Ariyarajah  A, Blake  IM, Dorigatti  I, Eckmanns  T, et al. Heterogeneities in the case fatality ratio in the West African Ebola outbreak 2013–2016. Philos Trans R Soc Lond B Biol Sci. 2017;372:20160308.
  6. Kucharski  AJ, Edmunds  WJ. Case fatality rate for Ebola virus disease in west Africa. Lancet. 2014;384:1260. DOIPubMedGoogle Scholar
  7. Lipsitch  M, Donnelly  CA, Fraser  C, Blake  IM, Cori  A, Dorigatti  I, et al. Potential biases in estimating absolute and relative case-fatality risks during outbreaks. PLoS Negl Trop Dis. 2015;9:e0003846.
  8. Ghani  AC, Donnelly  CA, Cox  DR, Griffin  JT, Fraser  C, Lam  TH, et al. Methods for estimating the case fatality ratio for a novel, emerging infectious disease. Am J Epidemiol. 2005;162:47986. DOIPubMedGoogle Scholar
  9. 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 Eng J Med. 2020;382:11991207.
  10. 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;13:37. DOIPubMedGoogle Scholar
  11. 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;395:68997. DOIPubMedGoogle Scholar
  12. Abbott  S, Hellewell  J, Munday  J, Funk  S; CMMID nCoV working group. The transmissibility of novel Coronavirus in the early stages of the 2019-20 outbreak in Wuhan: Exploring initial point-source exposure sizes and durations using scenario analysis. Wellcome Open Res. 2020;5:17. DOIPubMedGoogle Scholar
  13. Anastassopoulou  C, Russo  L, Tsakris  A, Siettos  C. Data-based analysis, modelling and forecasting of the COVID-19 outbreak. PLoS ONE. 2020;15:e0230405.
  14. Riou  J, Althaus  CL. Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020. Eurosurveillance. 2020 Jan 30 [cited 2020 Mar 6].
  15. 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;368:395400.
  16. <jrn>16. 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. </jrn>
  17. Sanche  S, Lin  YT, Xu  C, Romero-Severson  E, Hengartner  N, Ke  R. High contagiousness and rapid spread of severe acute respiratory syndrome coronavirus 2. Emerg Infect Dis. 2020;26:14707.
  18. Du  Z, Wang  L, Cauchemez  S, Xu  X, Wang  X, Cowling  BJ, et al. Risk for transportation of 2019 novel coronavirus disease from Wuhan to other cities in China. Emerg Infect Dis. 2020;26:104952.
  19. Bi  Q, Wu  Y, Mei  S, Ye  C, Zou  X, Zhang  Z, et al. Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study. Lancet Infect Dis. 2020;20:9119. DOIPubMedGoogle Scholar
  20. Song  QQ, Zhao  H, Fang  LQ, Liu  W, Zheng  C, Zhang  Y. [Study on assessing early epidemiological parameters of COVID-19 epidemic in China]. Zhonghua Liu Xing Bing Xue Za Zhi. 2020;41:4615.PubMedGoogle Scholar
  21. Jung  SM, Akhmetzhanov  AR, Hayashi  K, Linton  NM, Yang  Y, Yuan  B, et al. Real-time estimation of the risk of death from novel coronavirus (COVID-19) infection: inference using exported cases. J Clin Med. 2020;9:523. DOIPubMedGoogle Scholar
  22. 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;93:2014. DOIPubMedGoogle Scholar
  23. Lloyd-Smith  JO, Schreiber  SJ, Kopp  PE, Getz  WM. Superspreading and the effect of individual variation on disease emergence. Nature. 2005;438:3559. DOIPubMedGoogle Scholar
  24. Kucharski  AJ, Althaus  CL. The role of superspreading in Middle East respiratory syndrome coronavirus (MERS-CoV) transmission. Eurosurveillance. 2015;20:21167.
  25. Liu  Y, Eggo  RM, Kucharski  AJ. Secondary attack rate and superspreading events for SARS-CoV-2. Lancet. 2020;395:e47. DOIPubMedGoogle Scholar
  26. Kucharski  AJ, Russell  TW, Diamond  C, Liu  Y, Edmunds  J, Funk  S, et al.; Centre for Mathematical Modelling of Infectious Diseases COVID-19 working group. Early dynamics of transmission and control of COVID-19: a mathematical modelling study. Lancet Infect Dis. 2020;20:5538. DOIPubMedGoogle Scholar
  27. 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;92:6759.
  28. Shim  E, Tariq  A, Choi  W, Lee  Y, Chowell  G. Transmission potential and severity of COVID-19 in South Korea. Int J Infect Dis. 2020;93:33944. DOIPubMedGoogle Scholar
  29. Mizumoto  K, Chowell  G. Transmission potential of the novel coronavirus (COVID-19) onboard the diamond Princess Cruises Ship, 2020. Infect Dis Model. 2020;5:26470. DOIPubMedGoogle Scholar
  30. Backer  JA, Klinkenberg  D, Wallinga  J. Incubation period of 2019 novel coronavirus (2019-nCoV) infections among travellers from Wuhan, China, 20-28 January 2020. Euro Surveill. 2020;25:2000062. DOIPubMedGoogle Scholar
  31. Linton  NM, Kobayashi  T, Yang  Y, Hayashi  K, Akhmetzhanov  AR, Jung  SM, et al. Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data. J Clin Med. 2020;9:538. DOIPubMedGoogle Scholar
  32. Leung  C. The difference in the incubation period of 2019 novel coronavirus (SARS-CoV-2) infection between travelers to Hubei and nontravelers: The need for a longer quarantine period. Infect Control Hosp Epidemiol. 2020;41:5946. DOIPubMedGoogle Scholar
  33. Zhang  J, Litvinova  M, Wang  W, Wang  Y, Deng  X, Chen  X, et al. Evolving epidemiology and transmission dynamics of coronavirus disease 2019 outside Hubei province, China: a descriptive and modelling study. Lancet Infect Dis. 2020;20:793802.
  34. Du  Z, Xu  X, Wu  Y, Wang  L, Cowling  BJ, Meyers  LA. Serial interval of COVID-19 among publicly reported confirmed cases. Emerg Infect Dis. 2020;26:13413.
  35. Nishiura  H, Linton  NM, Akhmetzhanov  AR. Serial interval of novel coronavirus (COVID-19) infections. Int J Infect Dis. 2020;93:2846. DOIPubMedGoogle Scholar
  36. Ganyani  T, Kremer  C, Chen  D, Torneri  A, Faes  C, Wallinga  J, et al. Estimating the generation interval for coronavirus disease (COVID-19) based on symptom onset data, March 2020. Eurosurveillance. 2020;25:2000257.
  37. WHO–China Joint Mission on COVID-19. Report of the WHO-China Joint Mission on Coronavirus Disease 2019 (COVID-19). 2020 Feb [cited 2020 Mar 1].
  38. Guan  W, Ni  Z, Hu  Y, Liang  W, Ou  C, He  J, et al. Clinical characteristics of coronavirus disease 2019 in China. N Engl J Med. 2020;382:170820. DOIGoogle Scholar
  39. Verity  R, Okell  LC, Dorigatti  I, Winskill  P, Whittaker  C, Imai  N, et al. Estimates of the severity of coronavirus disease 2019: a model-based analysis. Lancet Infect Dis. 2020;20:66977. DOIPubMedGoogle Scholar
  40. Van Cuong  L, Giang  HTN, Linh  LK, Shah  J, Van Sy  L, Hung  TH, et al. The first Vietnamese case of COVID-19 acquired from China. Lancet Infect Dis. 2020;20:4089. DOIPubMedGoogle Scholar
  41. Pan  X, Chen  D, Xia  Y, Wu  X, Li  T, Ou  X, et al. Asymptomatic cases in a family cluster with SARS-CoV-2 infection. Lancet Infect Dis. 2020;20:4101. DOIPubMedGoogle Scholar
  42. Liu  Y-C, Liao  C-H, Chang  C-F, Chou  C–C, Lin  Y-R. A locally transmitted case of SARS-CoV-2 infection in Taiwan. N Engl J Med. 2020;382:10702.
  43. Pongpirul  WA, Pongpirul  K, Ratnarathon  AC, Prasithsirikul  W. Journey of a Thai taxi driver and novel coronavirus. N Engl J Med. 2020;382:10678. DOIPubMedGoogle Scholar
  44. Phan  LT, Nguyen  TV, Luong  QC, Nguyen  TV, Nguyen  HT, Le  HQ, et al. Importation and human-to-human transmission of a novel coronavirus in Vietnam. N Engl J Med. 2020;382:8724. DOIPubMedGoogle Scholar
  45. Russell  T, Hellewell  J, Jarvis  CI, van Zandvoort  K, Abbott  S, Ratnayake  R, et al. Estimating the infection and case fatality ratio for COVID-19 using age-adjusted data from the outbreak on the Diamond Princess cruise ship, March 2020. Euro Surveill. 2020;25:2000256.
  46. Fraser  C, Donnelly  CA, Cauchemez  S, Hanage  WP, Van Kerkhove  MD, Hollingsworth  TD, et al.; WHO Rapid Pandemic Assessment Collaboration. Pandemic potential of a strain of influenza A (H1N1): early findings. Science. 2009;324:155761. DOIPubMedGoogle Scholar
  47. Gire  SK, Goba  A, Andersen  KG, Sealfon  RSG, Park  DJ, Kanneh  L, et al. Genomic surveillance elucidates Ebola virus origin and transmission during the 2014 outbreak. Science. 2014;345:136972. DOIPubMedGoogle Scholar
  48. Rambaut  A, Holmes  E. The early molecular epidemiology of the swine-origin A/H1N1 human influenza pandemic. PLoS Curr. 2009;1:RRN1003. DOIPubMedGoogle Scholar
  49. Drummond  AJ, Ho  SYW, Phillips  MJ, Rambaut  A. Relaxed phylogenetics and dating with confidence. PLoS Biol. 2006;4:e88. DOIPubMedGoogle Scholar
  50. Huang  C, Wang  Y, Li  X, Ren  L, Zhao  J, Hu  Y, et al. Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China. Lancet. 2020;395:497506. DOIPubMedGoogle Scholar
  51. Hellewell  J, Abbott  S, Gimma  A, Bosse  NI, Jarvis  CI, Russell  TW, et al. Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob Health. 2020;8:e48896.
  52. Quilty  BJ, Clifford  S, Flasche  S, Eggo  RM, CMMID nCoV Working Group 2. Effectiveness of airport screening at detecting travellers infected with novel coronavirus (2019-nCoV). Euro Surveill. 2020;25:2000080.
  53. Tian  H, Liu  Y, Li  Y, Wu  C-H, Chen  B, Kraemer  MUG, et al. An investigation of transmission control measures during the first 50 days of the COVID-19 epidemic in China. Science. 2020;368:63842.
  54. Anzai  A, Kobayashi  T, Linton  NM, Kinoshita  R, Hayashi  K, Suzuki  A, et al. Assessing the impact of reduced travel on exportation dynamics of novel coronavirus infection (COVID-19). J Clin Med. 2020;9:601. DOIPubMedGoogle Scholar
  55. Kwok  KO, Li  KK, Chan  HHH, Yi  YY, Tang  A, Wei  WI, et al. Community responses during early phase of COVID-19 epidemic, Hong Kong. Emerg Infect Dis. 2020;26:15759.
  56. Kraemer  MUG, Yang  C-H, Gutierrez  B, Wu  C-H, Klein  B, Pigott  DM, et al.; Open COVID-19 Data Working Group. The effect of human mobility and control measures on the COVID-19 epidemic in China. Science. 2020;368:4937. DOIPubMedGoogle Scholar
  57. Cameron  E, Nuzzo  J, Bell  J, Nalabandian  M, O’Brien  J, League  A, et al. Global Health Security Index. Washington (DC): NTI and Johns Hopkins Center for Health Security; 2019 [cited 2020 Mar 1].
  58. Lipsitch  M, Cohen  T, Cooper  B, Robins  JM, Ma  S, James  L, et al. Transmission dynamics and control of severe acute respiratory syndrome. Science. 2003;300:196670. DOIPubMedGoogle Scholar
  59. Garske  T, Legrand  J, Donnelly  CA, Ward  H, Cauchemez  S, Fraser  C, et al. Assessing the severity of the novel influenza A/H1N1 pandemic. BMJ. 2009;339:b2840.
  60. Zou  L, Ruan  F, Huang  M, Liang  L, Huang  H, Hong  Z, et al. SARS-CoV-2 viral load in upper respiratory specimens of infected patients. N Engl J Med. 2020;382:11779.
  61. Yu  P, Zhu  J, Zhang  Z, Han  Y. A familial cluster of infection associated with the 2019 novel coronavirus indicating possible person-to-person transmission during the incubation period. J Infect Dis. 2020;221:175761.
  62. Tong  Z-D, Tang  A, Li  K-F, Li  P, Wang  H-L, Yi  J-P, et al. Potential presymptomatic transmission of SARS-CoV-2, Zhejiang Province, China, 2020. Emerg Infect Dis. 2020;26:10524. DOIPubMedGoogle Scholar
  63. Bai  Y, Yao  L, Wei  T, Tian  F, Jin  D-Y, Chen  L, et al. Presumed asymptomatic carrier transmission of COVID-19. JAMA. 2020;323:14067.
  64. Hu  Z, Song  C, Xu  C, Jin  G, Chen  Y, Xu  X, et al. Clinical characteristics of 24 asymptomatic infections with COVID-19 screened among close contacts in Nanjing, China. Sci China Life Sci. 2020;63:70611. DOIPubMedGoogle Scholar

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1All authors contributed equally to this article.

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