Abstract
The SIJR model, simplified from the SEIJR model, is adopted to analyze the important parameters of the model of SARS epidemic such as the transmission rate, basic reproductive number. And some important parameters are obtained such as the transmission rate by applying this model to analyzing the situation in Hong Kong, Singapore and Canada at the outbreak of SARS. Then forecast of the transmission of SARS is drawn out here by the adjustment of parameters (such as quarantined rate) in the model. It is obvious that inflexion lies on the crunode of the graph, which indicates the big difference in transmission characteristics between the epidemic under control and not under control. This model can also be used in the comparison of the control effectiveness among different regions. The results from this model match well with the actual data in Hong Kong, Singapore and Canada and as a by-product, the index of the effectiveness of control in the later period can be acquired. It offers some quantitative indexes, which may help the further research in epidemic diseases.
Keywords: SARS, quarantined rate, transmission rate, basic reproductive number, SIJR model, SEIJR model, inflexion
References
- 1.Enserink Martin. One year after outbreak, SARS virus yields some secrets. Science. 2004;304:1097–1097. doi: 10.1126/science.304.5674.1097. [DOI] [PubMed] [Google Scholar]
- 2.Chowell, G., Fenimore, P. W., Castillo-Garsow, M. A. et al., SARS outbreak in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism, Los Alamos Unclassified Report LA-UR-03-2653, 2003. [DOI] [PMC free article] [PubMed]
- 3.Lipsitch Marc, Cohen Ted, Cooper Ben, et al. Transmission dynamics and control of sever acute respiratory syndrome. Science. 2003;300:1966–1970. doi: 10.1126/science.1086616. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 4.Riley Steven, Fraser Christophe, Donnelly Christ A., et al. Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions. Science. 2003;300:1961–1966. doi: 10.1126/science.1086478. [DOI] [PubMed] [Google Scholar]
- 5.Dye Chris, Gay Nigel. Modeling the SARS epidemic. Science. 2003;300:1884–1885. doi: 10.1126/science.1086925. [DOI] [PubMed] [Google Scholar]
- 6.Qizhi Chen. Stochastic model application in SARS forecast and epidemic analysis. University of Peking College Journal (Medical Science Version) 2003;35(z1):75–80. [Google Scholar]
- 7.Scholzen, A., Wird ganz Hongkong von SARS erfasst? Wissenschaftler bef ü rchten dramatischen Anstieg der Lungenseuche, Die Welt, April 10, 2003: 32.
- 8.Razum Oliver, Becher Heiko, Kapaun Annette, et al. SARS, lay epidemiology, and fear. Lancet. 2003;361(9370):1739–1740. doi: 10.1016/S0140-6736(03)13335-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9.Donnelly Christl A., Ghani Azra C., Leung Gabriel M., et al. Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong. Lancet. 2003;361(9371):1761–1766. doi: 10.1016/S0140-6736(03)13410-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 10.Ng Tuen Wai, Turinici Gabriel, Danchin Antoine. A double epidemic model for the SARS propagation. BMC Infectious Diseases. 2003;3:19–19. doi: 10.1186/1471-2334-3-19. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 11.Aron J. L., Schwartz I. B. Seasonality and period-doubling bifurcations in an epidemic model. J. Theory. Biol. 1984;110:665–679. doi: 10.1016/S0022-5193(84)80150-2. [DOI] [PubMed] [Google Scholar]
- 12.Earn J. D., Rohani P., Bolker B. M., et al. A simple model for complex dynamical transitions in epidemics. Science. 2000;287:667–670. doi: 10.1126/science.287.5453.667. [DOI] [PubMed] [Google Scholar]
- 13.Li, M. Y., Wang, L. C., Global Stability in Some SEIR Epidemic Models, IMA Volumes in Mathematics and Its Applications 126, Springer-Verlag, 2001, 295–311.
- 14.Ronald Gallant, George Tauchen, Efficient Method of Moments, Duke Economics Working Paper #02-06.
- 15.Gani Raymond, Leach Steve. Transmission potential of smallpox in contemporary populations. Nature. 2000;414:748–751. doi: 10.1038/414748a. [DOI] [PubMed] [Google Scholar]
- 16.Alves D., Haas V. J., Caliri A. The predictive power of R0 in an epidemic probabilistic system. Journal of Biological Physics. 2003;29(1):63–75. doi: 10.1023/A:1022567418081. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 17.Yang H. M. Population dynamics and the epidemiological model proposed by Severo. Tend?Encias em Matem′ atica Aplicada e Computacional. 2002;3(2):227–236. [Google Scholar]
- 18.Childs J. E., Curns A. T., Dey M. E., et al. Predicting the local dynamics of epizootic rabies among raccoons in the United States. Proc. Natl. Acad. Sci. USA. 2000;97(25):13666–13671. doi: 10.1073/pnas.240326697. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 19.Chowell G., Hengartner N. W., Castillo-Chavez C., et al. The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. J. Theor. Biol. 2003;229(1):119–126. doi: 10.1016/j.jtbi.2004.03.006. [DOI] [PubMed] [Google Scholar]
- 20.Leo Y. S., Chen M., Heng B. H., et al. Severe acute respiratory syndrome—Singapore. MMWR. 2003;18(52):405–411. [PubMed] [Google Scholar]