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

Abstract

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 Ro = 2.0, F = 20%, i = 5 days, d = 14 days. Conclusions: Using the proposed mathematical mode, 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.