Construction of food and water borne pathogens' dose-response curves using the expanded Fermi Solution

Theoretically, the relationship between the number of pathogens that cause acute infection if settling in the gut, N, and that initially ingested, M, can be constructed from the survival probabilities at the different "stations" along the digestive tract. These probabilities are rarely known exactly, but their ranges can be estimated. If for a given N one generates estimates of M using random probabilities within these ranges, the estimates' distribution will be approximately lognormal and its cumulative (CDF) form will represent the pathogen's dose-response curve. The distribution's logarithmic mean and standard deviation can be calculated from the ranges with a formula and used to plot the curve. The method was used to generate dose-response curves of hypothetical food and waterborne pathogens and calculate their infective dose (ID) at 5%, 50%, and 95% probability. The curves were compatible with the Beta Poisson model and robust against minor perturbations in the underlying probabilities' ranges. The calculation and plotting procedure was automated and posted on the Internet as a freely downloadable interactive Wolfram Demonstration. It allows the user to generate, modify, examine, and compare dose-response curves, and to calculate their characteristics, by moving sliders on the screen.