Incorporating Time-Dose-Response into Legionella Outbreak Models

A novel method was used to incorporate in vivo host–pathogen dynamics into a new robust outbreak model for legionellosis. Dose-response and time-dose-response (TDR) models were generated for Legionella longbeachae exposure to mice via the intratracheal route using a maximum likelihood estimation approach. The best-fit TDR model was then incorporated into two L. pneumophila outbreak models: an outbreak that occurred at a spa in Japan, and one that occurred in a Melbourne aquarium. The best-fit TDR from the murine dosing study was the beta-Poisson with exponential-reciprocal dependency model, which had a minimized deviance of 32.9. This model was tested against other incubation distributions in the Japan outbreak, and performed consistently well, with reported deviances ranging from 32 to 35. In the case of the Melbourne outbreak, the exponential model with exponential dependency was tested against non-time-dependent distributions to explore the performance of the time-dependent model with the lowest number of parameters. This model reported low minimized deviances around 8 for the Weibull, gamma, and lognormal exposure distribution cases. This work shows that the incorporation of a time factor into outbreak distributions provides models with acceptable fits that can provide insight into the in vivo dynamics of the host-pathogen system.