Skip to main content
PMC home page
Springer Nature - PMC COVID-19 Collection logoLink to Springer Nature - PMC COVID-19 Collection
. 2004;49(17):1819–1823. doi: 10.1007/BF03183407

The outbreak pattern of the SARS cases in Asia

Zhibin Zhang 1,✉, Chengfa Sheng 1, Zufei Ma 1, Dianmo Li 1
PMCID: PMC7089107  PMID: 32214712

Abstract

The severe acute respiratory syndrome (SARS) caused tremendous damage to many Asia countries, especially China. The transmission process and outbreak pattern of SARS is still not well understood. This study aims to find a simple model to describe the outbreak pattern of SARS cases by using SARS case data commonly released by governments. The outbreak pattern of cumulative SARS cases is expected to be a logistic type because the infection will be slowed down due to the increasing control effort by people and/or due to depletion of susceptible individuals. The increase rate of SARS cases is expected to decrease with the cumulative SARS cases, as described by the traditional logistical model, which is widely used in population dynamic studies. The instantaneous rate of increases were significantly and negatively correlated with the cumulative SARS cases in mainland of China (including Beijing, Hebei, Tianjin, Shanxi, the Autonomous Region of Inner Mongolia) and Singapore. The basic reproduction numberR 0 in Asia ranged from 2.0 to 5.6 (except for Taiwan, China). TheR 0 of Hebei and Tianjin were much higher than that of Singapore, Hongkong, Beijing, Shanxi, Inner Mongolia, indicating SARS virus might have originated differently or new mutations occurred during transmission. We demonstrated that the outbreaks of SARS in many regions of Asia were well described by the logistic model, and the control measures implemented by governments are effective. The maximum instantaneous rate of increase, basic reproductive number, and maximum cumulative SARS cases were also calculated by using the logistic model.

Keywords: severe acute respiratory syndrome (SARS), outbreak, epidemiology, logistic model

References

  • 1.Lipsitch, M. et al., Transmission dynamics and control of severe acute respiratory syndrome, Science, 300: 1966–1970. [DOI] [PMC free article] [PubMed]
  • 2.Riley, S. et al., Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions, Science, 300: 1961–1966. [DOI] [PubMed]
  • 3.Dye C., Gay N. Modeling the SARS Epidemic. Science. 2003;300(5627):1884–1885. doi: 10.1126/science.1086925. [DOI] [PubMed] [Google Scholar]
  • 4.Wallinga J., Edmunds W. J., Kretzchmar M. Perspective: human contact patterns and the spread of airborne infection disease. Trends in Microbiology. 1999;9:372–377. doi: 10.1016/S0966-842X(99)01546-2. [DOI] [PubMed] [Google Scholar]
  • 5.Diekmann O., Heesterbeek H., Metz J. A. J. On the definition and computation of the basic reproductive ratioR0 in the models for infectious diseases in the heterogeneous populations. J. Math. Biol. 1990;28:365–382. doi: 10.1007/BF00178324. [DOI] [PubMed] [Google Scholar]
  • 6.Hethcote H. W., van den Driesssche P. An SIS epidemic model with variable population size and a delay. J. Math. Biol. 1995;54:177–194. doi: 10.1007/BF00178772. [DOI] [PubMed] [Google Scholar]
  • 7.Becker N. G. Analysis of Infectious Disease Data. London: Chapman and Hall; 1989. [Google Scholar]
  • 8.Becker N. G. Parametric inference for epidemic models. Math. Biosci. 1993;117:239–239. doi: 10.1016/0025-5564(93)90026-7. [DOI] [PubMed] [Google Scholar]
  • 9.Becker N. G., Britton T. Statistical studies of infectious disease incidence. Stat. Soc. Series B. 1999;61:287–287. doi: 10.1111/1467-9868.00177. [DOI] [Google Scholar]
  • 10.Kramer I. Accurately simulating the growth in the size of the HIV infected population in AIDS epidemic country: Computing the USA HIV infection curve. Mathematical and Computer Modeling. 1994;19:91–112. doi: 10.1016/0895-7177(94)90052-3. [DOI] [Google Scholar]
  • 11.Yip P. Estimating the initial relative infection rate for a stochastic epidemic model. Theoretical Population Biology. 1989;36:202–202. doi: 10.1016/0040-5809(89)90030-0. [DOI] [PubMed] [Google Scholar]
  • 12.Shao Q. X. Some properties of an estimator for the basic reproductive number of a general epidemic model. Math. Biosci. 1999;159:79–96. doi: 10.1016/S0025-5564(99)00009-7. [DOI] [PubMed] [Google Scholar]
  • 13.O’Neill P. D. A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov Chain Monte Carlo methods. Math. Biosci. 2002;180:103–114. doi: 10.1016/S0025-5564(02)00109-8. [DOI] [PubMed] [Google Scholar]
  • 14.Zhang Z., Pech R., Davis S., Shi D., et al. Extrinsic and intrinsic factors determine the eruptive dynamics of Brandt’s volesMicrotus brandti in Inner Mongolia, China. Oikos. 2003;100:299–310. doi: 10.1034/j.1600-0706.2003.11810.x. [DOI] [Google Scholar]
  • 15.Bailei N. T. T. The Mathematical Theory of Diseases. 2nd edition. London: Griffin; 1975. [Google Scholar]
  • 16.Anderson R. M., May R. M. Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford Univ. Press; 1992. [Google Scholar]
  • 17.Capasso V., Serio G. A generalization of the Kermack-McKendrick deterministic epidemic model. Math. Biosci. 1978;42:43–61. doi: 10.1016/0025-5564(78)90006-8. [DOI] [Google Scholar]
  • 18.Mollison D. Epidemic Models: Their Structure and Relation to Data. Cambridge: Cambridge Univ. Press; 1995. [Google Scholar]
  • 19.Keepling M. J., Rand D. A., Morris A. J. Correlation models for childhood epidemics. Proc. R. Soc. Lond. 1997;264:1149–1149. doi: 10.1098/rspb.1997.0159. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 20.Ball F., Neal P. A general model for stochastic SIR epidemics with two level of mixing. Math. Biosci. 2002;180:73–102. doi: 10.1016/S0025-5564(02)00125-6. [DOI] [PubMed] [Google Scholar]
  • 21.Greenhalgh D., Diekmann O., de Jong M. C. M. Subcritical endemic steady states in mathematical models for animal infectious with incomplete immunity. Math. Biosci. 2000;165:1–25. doi: 10.1016/S0025-5564(00)00012-2. [DOI] [PubMed] [Google Scholar]
  • 22.Méndez V. M., Fort J. Dynamical evolution of discrete epidemic models. Physica A: Statistical Mechanics and Its Applications. 2000;284:309–317. doi: 10.1016/S0378-4371(00)00210-7. [DOI] [Google Scholar]
  • 23.Moghadas S. M. Global stability of two-stage epidemic model with generalized non-linear incidence. Mathematics and Computers in Simulation. 2002;60:107–118. doi: 10.1016/S0378-4754(02)00002-2. [DOI] [Google Scholar]
  • 24.Wendi W., Zhien M. Global dynamics of an epidemic model with time delay. Nonlinear Analysis: Real World Applications. 2002;3:365–373. doi: 10.1016/S1468-1218(01)00035-9. [DOI] [Google Scholar]
  • 25.Ruan S., Wang W. Dynamical behavior of an epidemic model with a nonlinear incidence rate. Journal of Differential Equations. 2003;188:135–163. doi: 10.1016/S0022-0396(02)00089-X. [DOI] [Google Scholar]
  • 26.Yang H. M. SARS Control Manual (in Chinese) Beijing: Science Press; 2003. pp. 22–22. [Google Scholar]
  • 27.Wang W. D., Ruan S. G. Simulating the SARS outbreak in Beijing with limited data. Journal of Theoretical Biology. 2004;227:369–379. doi: 10.1016/j.jtbi.2003.11.014. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Chinese Science Bulletin = Kexue Tongbao are provided here courtesy of Nature Publishing Group

RESOURCES