THEORY AND METHODS

A simple approximate mathematical model to predict the number of severe acute respiratory syndrome cases and deaths

B C K Choi¹, A W P Pak²

¹ Department of Epidemiology and Community Medicine, Faculty of Medicine, University of Ottawa, Ottawa, Ontario, Canada and Department of Public Health Sciences, Faculty of Medicine, University of Toronto, Toronto, Ontario, Canada
² Institutional Research and Planning, University of Ottawa, Canada

Correspondence to:
Correspondence to:
Dr B C K Choi
432 Pleasant Park Road, Ottawa, Ontario, Canada K1H 5N1; Bernard.Choi{at}utoronto.ca

Background: Severe acute respiratory syndrome (SARS) is currently spreading in many countries. This paper proposes a simple approximate mathematical model for public health practitioners to predict the number of SARS cases and deaths.

Methods: The model is based on four parameters: R_o (basic reproductive number), F (case-fatality rate), i (incubation period), and d (duration of disease). The calculations can be done by hand or by using a computer spreadsheet.

Results: The best parameters to fit Canadian data as of 6 April 2003 (before infection controls took effect) are R_o = 1.5, F = 30%, i = 5 days, d = 14 days. On 6 April (day 40) there were 74 cases and 7 deaths. If this trend continues, SARS numbers in Canada are predicted to be as follows: 387 cases and 34 deaths by 26 April (day 60), 4432 cases and 394 deaths by 26 May (day 90), and 50 500 cases and 4489 deaths by 25 June (day 120). By comparison, the best parameters to fit Hong Kong data as of 10 April 2003 are R_o = 2.0, F = 20%, i = 5 days, d = 14 days.

Conclusions: Using the proposed mathematical model, it was estimated that about 1.5 to 2 new infectious cases were produced per infectious case every five days. Also, about 20% to 30% of the cases die within 14 days. The case-fatality may therefore be considerably higher than initially thought. The model indicates that SARS can spread very fast when there are no interventions.

Keywords: SARS; severe acute respiratory syndrome; infectious disease; prediction; statistics; modelling

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