We analyzed temporal stability and geographic trends in cumulative case-fatality rates and average doubling times of severe acute respiratory syndrome (SARS). In part, we account for correlations between case-fatality rates and doubling times through differences in control measures. Factors that may alter future estimates of case-fatality rates, reasons for heterogeneity in doubling times among countries, and implications for the control of SARS are discussed.

Concern over the emergence of severe acute respiratory syndrome (SARS) has persisted as epidemic continues in the first months of 2003, despite control efforts. As of May 12, 2003, the World Health Organization (WHO) had reported 7,447 cases with 552 deaths in >30 countries. The most affected locations are China, Hong Kong, Singapore, Viet Nam, Taiwan, and Canada. (Our study focuses on Canada.) Doubling times (i.e., the period required for the number of cases in the epidemic to double) and case-fatality rates (CFRs) are fundamental to the epidemiology and potential public health impact of SARS. Doubling times are a measure of the rate of spread of disease and also indicate the magnitude of control efforts required to curtail spread. Because doubling times change substantially over the course of an epidemic, current estimates should not be used to extrapolate into the future.

CFRs of SARS have typically been estimated by dividing the number of deaths by the total number of cases. This method is sufficient for an advanced epidemic. However, the method is not accurate at an early stage of an epidemic, particularly when the time from infection to recovery or death is not brief, relative to the duration of the epidemic, as is currently true with SARS. The method underestimates the CFR because it does not account for a proportion of currently infected persons’ dying from the disease. A more accurate method would be to divide the number of deaths by the total number of deaths plus the number of persons who recovered. By applying this method to publicly available WHO data (

Cumulative case-fatality rates for severe acute respiratory syndrome over time.

Average overall CFR for all countries increased from 10.4% on April 21 to 14.7% on May 12 (largely attributable to the sudden rise in CFRs in China and Taiwan). In countries with few deaths, this estimate of CFR may be a slight overestimate if the time from infection to death tends to be shorter than time to recovery. However, recent cohort data from Hong Kong (

We identify an inverse relationship between the average CFR and the average doubling time for different countries (_{2} of the relative growth in numbers of reported cases during the same period; see

Cumulative case-fatality rate for severe acute respiratory syndrome compared with average doubling time as of May 12, 2003.

Variation in CFRs among countries will arise from differences in intensity and speed of medical care, age structure of the population (older infected patients are more likely to die [

Estimates of CFR may change as polymerase chain reaction (PCR) assays become more widely used in diagnosis (

As an epidemic declines, the doubling time increases. Variation in doubling time among countries probably arises from variation in both transmission rates and control efforts (^{-1}) is determined by the expected number of susceptible persons with whom each infectious person comes into contact during a time unit in their infectious periods and by the probability of disease transmission per contact. High-density population centers, crowded public transportation systems, and hospital waiting rooms increase the number of contacts, while personal hygiene affects the probability that transmission will occur with each contact. In all countries, seasonal effects may also play a substantial role with the virus spreading faster in winter.

Time series of log of average doubling time for severe acute respiratory syndrome.

In Viet Nam, the doubling time increased over the period that the epidemic was being controled (

Epidemic models may provide a framework for evaluating alternative control measures. Central to the accurate parameterization of epidemic models is the reproductive ratio, _{0}, which is the average number of secondary cases generated by one initial infection in a susceptible population in the absence of control measures (_{0} defines a threshold that determines whether an infection is likely to spread. If _{0} is <1, each infection will not replace itself, on average, and the disease will likely die out, although in such cases spatial dynamics, latency, and stochastic variation may contribute to localized flare-ups of the disease that may persist for a long time. Thus, _{0} also defines the level of intervention required to contain an epidemic. The doubling rate can be used to calculate _{0,} given that_{0}. Typical estimates of the incubation period for SARS range from approximately 2 to 10 days (median and mean 5 days) (_{0} from doubling times since the latter is confounded by evolving control policies (e.g., Hong Kong, Toronto); the most natural epidemic (in Guangdong Province) offers the least complete data.

Observed and expected cumulative number of cases of severe acute respiratory syndrome in China.

The rapid increase in the number of cases in China suggests an urgent need to control the epidemic in Asia before it gains further momentum. Containment of an outbreak at an early stage affords a greater chance of success than does a later response and clearly puts less strain on the healthcare system. Isolation of cases, infection-control measures in hospitals, and vigilant surveillance at community and population levels are imperative. Failing this, SARS could become endemic in China, particularly if it evolves antigenically to evade pre-existing immunity, such that recovered patients could be reinfected, as is the case for influenza (

Severe Acute Respiratory Syndrome: Temporal Stability and Geographic Variation in Case-Fatality Rates and Doubling Times

We thank A. Reingold for helpful discussions.

Dr. Galvani is a Miller Research Fellow at University of California, Berkeley. Her primary research interests are focused on the evolution and epidemiology of infectious diseases, including influenza.