Expanded Fermi solution for estimating the survival of ingested pathogenic and probiotic microbial cells and spores

The expanded Fermi solution was originally developed for estimating the number of food-poisoning victims when information concerning the circumstances of exposure is scarce. The method has been modified for estimating the initial number of pathogenic or probiotic cells or spores so that enough of them will survive the food preparation and digestive tract's obstacles to reach or colonize the gut in sufficient numbers to have an effect. The method is based on identifying the relevant obstacles and assigning each a survival probability range. The assumed number of needed survivors is also specified as a range. The initial number is then estimated to be the ratio of the number of survivors to the product of the survival probabilities. Assuming that the values of the number of survivors and the survival probabilities are uniformly distributed over their respective ranges, the sought initial number is construed as a random variable with a probability distribution whose parameters are explicitly determined by the individual factors' ranges. The distribution of the initial number is often approximately lognormal, and its mode is taken to be the best estimate of the initial number. The distribution also provides a credible interval for this estimated initial number. The best estimate and credible interval are shown to be robust against small perturbations of the ranges and therefore can help assessors achieve consensus where hard knowledge is scant. The calculation procedure has been automated and made freely downloadable as a Wolfram Demonstration.