Many severe acute respiratory syndrome (SARS) patients have multiple possible incubation periods due to multiple contact dates. Multiple contact dates cannot be used in standard statistical analytic techniques, however. I present a simple spreadsheet-based method that uses multiple contact dates to calculate the possible incubation periods of SARS.

The appearance and rapid spread of severe acute respiratory syndrome (SARS), caused by a previously unknown coronavirus (SARS-CoV) (

To make quarantine and isolation as effective as possible, knowing the range of the possible incubation period of SARS is essential. Mathematical modelers also need to know the characteristics of the incubation period to provide estimates of possible spread and model the potential impact of interventions. Many SARS patients often report more than one possible date of contact with another known SARS patient (

Patient source and no.^{a} | Possible incubation period of SARS in days | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |

Canada 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |||||||

Canada 2 | 1 | 2 | 3 | 4 | ||||||||||||||

Canada 3 | 1 | 4 | ||||||||||||||||

Canada 4 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |||||||

Canada 5 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | ||||

Canada 7 | 3 | 10 | ||||||||||||||||

Canada 8^{b} | 3 | |||||||||||||||||

Canada 10 | 1 | 2 | 3 | 4 | 5 | 6 | ||||||||||||

Hong Kong 2 | 2 | |||||||||||||||||

Hong Kong 3 | 2 | |||||||||||||||||

Hong Kong 4 | 6 | |||||||||||||||||

Hong Kong 5 | 2 | |||||||||||||||||

Hong Kong 6 | 1 | 2 | 3 | 4 | 5 | 6 | ||||||||||||

Hong Kong 7 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |||||||||||

Hong Kong 8 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |||||||||||

Hong Kong 9 | 1 | 2 | 3 | 4 | 5 | |||||||||||||

Hong Kong 10 | 2 | 3 | 4 | 5 | 6 | 7 | ||||||||||||

USA 1 | 6 | 13 | 14 | 15 | 16 | 17 | 18 | |||||||||||

USA 2 | 7 | 8 | 9 | 10 | 11 | 12 |

^{a}Patient source: Canada refers to patients reported in reference ^{b}Patient 9 from the Canadian database (

I present a simple method that allows a simulation of the frequency distribution, including confidence intervals, of the possible incubation periods (in days) for SARS. The method allows use of data from patients with multiple potential incubation periods. One goal of the method was to keep it simple by using common computer spreadsheet software, allowing for easy replication, extension of the database and results, and rapid dissemination of the method. The method can also be used to calculate when infectious persons are most likely to have transmitted SARS to susceptible persons, even when multiple days of possible transmission exist.

I used published data reporting possible incubation periods for 17 patients (

During a single iteration, for each patient, the programmed model selects the incubation period with the highest random number for that iteration. After a single iteration, the program calculates the frequency distribution for the incubation periods. Then, the program assigns another set of random numbers to each possible incubation period and selects and calculates the frequency distribution. After numerous iterations, the program combines all the frequency distributions from all iterations to provide a general frequency distribution. From this final frequency distribution, descriptive statistics can be obtained, such as the mean, median, 5th and 95th percentile values. I ran approximately 10,000 iterations, at which point each additional iteration caused the mean and the standard distribution for each possible day of incubation to change by <1%.

The three largest mean frequencies of incubation periods among the patients examined were 2, 3, and 6 days (

Simulation of frequency distribution of incubation period of severe acute respiratory syndrome. Data used for this simulation were obtained from Canada (

Cumulative frequency incubation period of severe acute respiratory syndrome. Data are the mean frequencies of each individual incubation period, as shown in

The incubation period for SARS is likely to be varied, with the frequency distribution being nonnormal (

Given that data from only 19 patients were available for this analysis, some caution should be exercised when evaluating the results. Adding or subtracting relatively small numbers of patients can cause estimates such as the 95th percentile of the cumulative frequency to change. More data concerning the possible incubation period of SARS patients are needed. The advantage of the method used here is that such data need not be specific. The method readily “accepts” data in which patients have multiple possible incubation periods. More data will likely reduce the confidence intervals for the frequencies of each incubation day (

The method can also be readily adapted to examine other aspects of SARS epidemiology when unambiguous data are scarce. For example, with the appropriate data, this method can be used to examine the frequency distribution of when an infectious person infects other people. (An Excel workbook [Excel 2000, Microsoft, Corp, Redmond, WA] containing the model used to calculate the results shown in

Spreadsheet model to calculate incubation period of SARS

Dr. Meltzer is senior health economist in the Office of Surveillance, National Center for Infectious Diseases, Centers for Disease Control and Prevention. His research interests include studying the economics of interventions to control and prevent infectious diseases, and providing economic data to aid the planning for catastrophic infectious disease events.