A method for incorporating a time-dose-response model into a Giardia lamblia outbreak

Experimental time-to-infection data is a useful, but often underutilized, material for examining the mechanics of in vivo pathogen growth. In this paper, the authors attempt to incorporate a time-dose-response (TDR) equation into a model which predicts the number of ill persons per day in a Giardia lamblia epidemic using data collected from a Pittsfield, Massachusetts outbreak. To this end, dose-response and TDR models were generated for Giardia exposure to beaver and human volunteers, and a maximum likelihood estimation approach was used to ensure that the models provided acceptable fits. The TDR equation that best-fit the human data was the beta-Poisson with exponential-reciprocal dependency model, and this was chosen to be incorporated into the outbreak model. The outbreak model is an expanded probability model that convolutes an assumed incubation distribution of the infectious agent with an exposure distribution. Since the beta-Poisson with exponential-reciprocal dependency models the time-to-infection density distribution, it is input as the incubation distribution. Several density functions, including the Weibull, lognormal, gamma, and uniform functions served as exposure distributions. The convolution of the time-dependent probability distribution with the lognormal distribution yielded the best-fit for the outbreak model.