Skip to main content
PMC home page
Wiley - PMC COVID-19 Collection logoLink to Wiley - PMC COVID-19 Collection
. 2008 Jul 9;50(4):597–607. doi: 10.1002/bimj.200710431

Bayesian Analysis of Severe Acute Respiratory Syndrome: The 2003 Hong Kong Epidemic

Phenyo E Lekone 1,✉
PMCID: PMC7161832  PMID: 18615412

Abstract

This paper analyzes data arising from a Severe Acute Respiratory Syndrome (SARS) epidemic in Hong Kong in 2003 involving 1755 cases. A discrete time stochastic model that uses a back‐projection approach is proposed. Markov Chain Monte Carlo (MCMC) methods are developed for estimation of model parameters. The algorithm is further extended to integrate numerically over unobserved variables of the model. Applying the method to SARS data from Hong Kong, a value of 3.88 with a posterior standard deviation of 0.09 was estimated for the basic reproduction number. An estimate of the transmission parameter at the beginning of the epidemic was also obtained as 0.149 with a posterior standard deviation of 0.003. A reduction in the transmission parameter during the course of the epidemic forced the effective reproduction number to cross the threshold value of one, seven days after control interventions were introduced. At the end of the epidemic, the effective reproduction number was as low as 0.001 suggesting that the epidemic was brought under control by the intervention measures introduced. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Keywords: Back‐projection, Bayesian inference, Control Intervention, SARS epidemics

References

  1. Becker, N. G. , Watson, L. F. , and Carlin, J. B. (1991). A method of non‐parametric back‐projection and its application to AIDS data. Statistics in Medicine 10, 1527–1542. [DOI] [PubMed] [Google Scholar]
  2. Becker, N. G. and Xu, C. (1994). Dependent HIV incidences in back‐projection of AIDS incidence data. Statistics in Medicine 13, 1945–1958. [DOI] [PubMed] [Google Scholar]
  3. Brookmeyer, R. and Gail, M. H. (1986). Minimum size of the acquired immunodeficiency syndrome (AIDS) epidemic in the United States. Lancet 2, 1320–1322. [DOI] [PubMed] [Google Scholar]
  4. Chau, P. H. and Yip, P. S. F. (2003a). Monitoring the severe acute respiratory syndrome epidemic and assessing effectiveness of interventions in Hong Kong Special Administrative Region. Journal of Epidemiology and Community Health 57, 766–769. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Chau, P. H. and Yip, P. S. F. (2003b). Modelling the severe acute respiratory syndrome. Hong Kong Medical Journal 9, 310–311. [PubMed] [Google Scholar]
  6. Chib, S. and Jeliazkov, I. (2001). Marginal likelihood from the Metropolis‐Hastings output. Journal of the American Statistical Association 96, 270–281. [Google Scholar]
  7. Chowell, G. , Fenimore, P. W. , Castillo‐Garsow, M. A. , and Castillo‐Chavez, C. (2003). SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism. Journal of Theoretical Biology 224, 1–8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Chowell, G. , Hengartner, N. W. , Castillo‐Chavez, C. , Fenimore, P. W. , and Hyman, J. M. (2004). The basic reproductive number of Ebola and the effects of public health measures: The cases of Congo and Uganda. Journal of Theoretical Biology 229, 119–126. [DOI] [PubMed] [Google Scholar]
  9. Diekmann, O. , Heesterbeek, J. A. , and Metz, J. A. (1990). On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 28, 365–382. [DOI] [PubMed] [Google Scholar]
  10. Donnelly, C. A. , Ghani, A. C. , Leung, G. M. , Hedley, A. J. , Fraser, C. , Riley, S. , Abu‐Raddad, L. J. , Ho, L. , Thach, T. , Chau, P. , Chan, K. , Lam, T. , Tse, L. , Tsang, T. , Liu, S. , Kong, J. H. B. , Lau, E. M. C. , Ferguson, N. M. , and Anderson, R. M. (2003). Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong. The Lancet 361, 1761–1766. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Doornik, J. A. (1999). Object‐orientated Matrix Programming using Ox version 2.1. Timberlake Consultants Limited, London.
  12. Gelman, A. , Meng, X. L. , and Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica 6, 733–807. [Google Scholar]
  13. Lekone, P. E. and Finkenstädt, B. F. (2006). Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 62, 1170–1177. [DOI] [PubMed] [Google Scholar]
  14. Leung, G. M. , Hedley, A. J. , Ho, L. , Chau, P. , Wong, I. O. L. , Thach, T. Q. , Ghani, A. C. , Donnelly, C. A. , Fraser, C. , Riley, S. , Ferguson, N. M. , Anderson, R. M. , Tsang, T. , Leung, P. , Wong, V. , Chan, J. C. K. , Tsui, E. , Lo, S. , and Lam, T. (2004). The epidemiology of severe acute respiratory syndrome in the 2003 Hong Kong epidemic: an analysis of all 1755 patients. Annals of Internal Medicine 141, 662–673. [DOI] [PubMed] [Google Scholar]
  15. Lipsitch, M. , Cohen, T. , Cooper, B. , Robins, J. M. , Ma, S. , James, L. , Gopalakrishma, G. , Chew, S. K. , Tan, C. C. , Samore, M. H. , Fisman, D. , and Murray, M. (2003). Transmission dynamics and control of severe acute respiratory syndrome. Science 300, 1966–1970. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. McBryde, E. S. , Gibson, G. , Pettitt, A. N. , Zhang, Y. , Zhao, B. , and McElwain, D. L. S. (2006). Bayesian modelling of an epidemic of severe acute respiratory syndrome. Bulletin of Mathematical Biology 68, 889–917. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Riley, S. , Fraser, C. , Donnelly, C. A. , Ghani, A. C. , Abbu‐Raddad, L. J. , Hedley, A. J. , Leung, G. M. , Ho, L. , Lam, T. , Thach, T. Q. , Chau, P. , Chan, K. , Lo, S. , Leung, P. , Tsang, T. , Ho, W. , Lee, K. , Lau, E. M. C. , and Ferguson, N. M. (2003). Transmission dynamics of the aetiological agent of severe acute respiratory syndrome (SARS) in Hong Kong: the impact of public health interventions. Science 300, 1961–1966. [DOI] [PubMed] [Google Scholar]
  18. Wallinga, J. and Teunis, P. (2004). Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. American Journal of Epidemiology 160, 509–516. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Biometrical Journal. Biometrische Zeitschrift are provided here courtesy of Wiley

RESOURCES