Stochastic modelling of the growth of a microbial population under changing temperature regimes

The application of models of microbial growth to the design of food safety systems requires consideration of the effect of arbitrary changes in external variables on growth of bacteria. In particular, the effect of changes in external variables, such as temperature, on the probability that the microbial population size will not exceed acceptable levels at a given time needs to be predicted. This paper presents a method of calculating the time-dependent probability distribution of the microbial population size under arbitrary changes of temperature through time. To illustrate this method, the effect of a sudden temporary increase in temperature on the evolution of the probability distribution of Lactobacillus plantarum population size is presented. The effect of this change in temperature on the time taken for the population to reach a critical size, with a given probability, is also calculated and the application of this calculation to the design of HACCP protocols is discussed.