Applications of Stochastic Processes to Microbial Risk Assessment. H. M. Marks and M. E. Coleman, US Department of Agriculture, Food Safety & Inspection Service, 1400 Independence Avenue, SW, Washington, DC 20250-3700
A critical component of a risk assessment is determining the uncertainty and population distribution of variables that are used for predicting risk. In microbial risk assessments most of the attention has been paid to developing deterministic models and predicting expected risks as a function of various factors. Because the microbial risk assessment involves dynamic modeling, dynamic mechanistic models have been used to model microbial growth. In the areas of predictive microbiology, modeling has concentrated on predicting the expected relative growth. Incorporating models that include uncertainty and population variability involve identifying the stochastic nature of the variables. There is a rich mathematical development of stochastic process and their application to microbiological growth. This paper provides an introduction and some examples of applying procedures of stochastic processes for estimating numbers of organisms in a precessing environment for a risk assessment. Models incorporating random components of cellular growth are discussed. In addition, mechanistic models of microbial growth in a processing environment are extended to include stochastic variation. Using the first two moments of the distribution, reasonable approximations to the distribution of the number of organisms can be obtained. When a significant probability of zero organisms exists, two probability distributions, the negative binomial and the extreme value distributions, are suggested for use as simple alternatives to the sometimes unknown or complicated exact distributions.
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