Quantitative epidemiology of SARS as reported from Singapore. (A) Epidemic curve for cases reported up to 5 May 2003. (B) The number of secondary cases infected by an index case reported by week (mean indicated by circles; minimum and maximum indicated by error bars); horizontal line indicates 1, the minimum for epidemic growth. (C) Time from onset of symptoms until hospital isolation of the case, stratified by week of onset. (D) Number of primary cases (green) by time from symptom onset to isolation, number of secondary cases infected by such cases (orange), and mean number of secondary cases per primary case. (E) Serial intervals for known transmissions in Singapore: time from onset of symptoms in index case to onset of symptoms in secondary case with fitted Weibull distribution. (F) Serial intervals stratified by week of onset in the index case. (B), (C), and (F) exclude the final week of data to avoid possible censoring bias. In the box-whisker plots [(C) and (F)], the box extends from the 25th to 75th percentile of observations [interquartile range (IQR)], with the center line indicating the median. The bars define the upper and lower adjacent values, defined as 75th percentile + 1.5 IQR and 25th percentile − 1.5 IQR. The circles denote observed points outside the adjacent values or single observations in a period.

Estimated values of the reproductive number for SARS in the absence of specific control measures for a range of serial intervals from 4 to 15 days (SOM Text). Figure assumes f = 0.3 or 0.7; see fig. S1 for sensitivity analysis for different values of f . Green represents estimated R values for Y(41 days) = 425; red, Y(63 days) = 1358; magenta, Y(185 days) = 7919; and blue, Y(185 days) = 15,000.

Marginal posterior distribution of R under the Bayesian procedure (11) for Y(41 days) = 425 based on 1000 simulations for each candidate value of R. The most notable feature of the posterior distribution is the considerable right skew, so that although the 90% credible interval spans (1.5, 7.7), the mode is about 2.2 and the expected value is 3.5. Thus, the mode is somewhat lower and the mean somewhat higher than the range obtained by the deterministic approach, which for a serial interval of 8.4 days is 2.2 to 2.6, depending on the value of f used.

The probability of an outbreak of SARS in a susceptible population for a range of values of R, approximated by the probability of nonextinction of a branching process (22) in which the number of secondary cases is given by a negative binomial distribution with a mean of R and a variance-to-mean ratio ranging from 1 (for which the negative binomial reduces to the Poisson distribution) to 20 [from left to right: 1 (black), 2 (green), 4 (blue), 10 (magenta), 20 (red)] after the introduction of (A) a single infectious case, (B) 5 infectious cases, (C) 20 infectious cases, and (D) 100 infectious cases.

Mathematical model for SARS transmission. Susceptible individuals are infected by infectious, undetected individuals and become infectious themselves after a stage of latency. Infectious individuals lose infectiousness by death, recovery, or isolation. No births or deaths from non-SARS causes are considered. When quarantine is implemented, a proportion, q, of new infections are quarantined before they become infectious; additionally, the same proportion of susceptible individuals who were contacts of infectious persons but were not infected are also quarantined. Susceptible individuals are released from quarantine after 10 days; for simplicity, we assume that quarantined individuals are isolated before they can infect anyone else and that compliance with quarantine is complete (SOM Text).

Modeled public-health impact of interventions against SARS including isolation and quarantine. (A) Contour plot showing values of the reproductive number with interventions, R_int, as a function of the proportion of contacts effectively quarantined (q) and the reduction in infectiousness achieved by infection control and isolation. The aim of these interventions is to curtail the epidemic by reducing R_int to less than 1. A baseline value of R = 3 is assumed. (B) The total number of days spent in quarantine per person during the entire course of a SARS epidemic for a given level of effective quarantine. A threshold exists above which quarantining a larger fraction of each infectious case's contacts lowers the number of person-days in quarantine. This threshold is lowered as the duration of infectiousness for each case is reduced by faster isolation, which is indicated by the number next to each curve. Absolute values are for illustration only as they depend on several unknown parameters (SOM Text).