Modeling Legionnaires' disease outbreaks: estimating the timing of an aerosolized release using symptom-onset dates.

BACKGROUND: Over the last 30 years, there have been a number of reported Legionnaires' disease outbreaks resulting from the release of causative organisms from aerosol-producing devices.
METHODS: We model a Legionnaires' disease epidemic curve as the convolution of an infection-time distribution (representing the aerosolized release) and an incubation-period distribution. The model is fitted to symptom-onset data from specific outbreaks to estimate the start and end dates of the release. We also develop this retrospective "back-calculation" model into a prospective "real-time" model that can estimate the final size of an ongoing outbreak, in addition to the timing of its release.
RESULTS: In the retrospective analysis, the estimated release end dates were generally earlier than reported end dates. This suggests that, in many outbreaks, the release might have already ended by the time the source was reportedly cleaned or closed. Prospective analysis showed that valid estimates of the release start date could be achieved early in the outbreak, the total number of cases could be reasonably determined shortly after the release had ended, and estimates of the release end date could be satisfactorily achieved in the latter stages of the outbreak.
CONCLUSIONS: This model could be used in the course of a Legionnaires' disease outbreak to provide early estimates of the total number of cases, thus helping to inform public-health planning. Toward the end of the outbreak, estimates of the release end date could help corroborate standard epidemiologic, environmental, and microbiologic investigations that seek to identify the source.