Modelling homogeneous and heterogeneous microbial contaminations in a powdered food product

The actual physical distribution of microorganisms within a batch of food influences quantification of microorganisms in the batch, resulting from sampling and enumeration by microbiological tests. Quantification may be most accurate for batches in which microorganisms are distributed homogeneously. However, when the distribution is non-homogeneous, quantification may result in an under-, or overestimation. In the case of pathogens being non-homogeneously distributed, this heterogeneity will impact on public health. Enumeration data are commonly modelled by the Lognormal distribution. Although the Lognormal distribution can model heterogeneity, it does not allow for complete absence of microorganisms. Studies that validate the appropriateness of using Lognormal or other statistical distributions are scarce. This study systematically investigated laboratory and industrial scale batches of powdered infant formula, modelled the enumeration data using a range of statistical distributions, and assessed the appropriateness of individual models. For laboratory scale experiments, batches of milk powder were contaminated by distributing similar numbers of cells of Cronobacter sakazakii either homogeneously throughout a batch of milk powder or by distributing the cells in a localised part of the batch. Each batch was then systematically sampled and the distribution determined by enumerating the samples. By also enumerating the remainder of the batch, a balance could be made of the total number of microorganisms added and of the number retrieved from a batch. Discrete, as well as continuous statistical distributions, were fitted to enumeration data and the parameters estimated by Maximum Likelihood. The data were fitted both as censored and uncensored data. Enumeration data obtained for an industrial batch of powdered infant formula were investigated in this way as well. It was found that Normal, Poisson and Zero-Inflated Poisson distributions fitted the data sets very poorly. In case of homogeneous contamination, there was not a notable difference between the ability of Negative Binomial, Poisson-Lognormal, Weibull, Gamma, and Lognormal distributions to model the data. Overall, either the Negative Binomial distribution or the Poisson-Lognormal distribution fitted the data best in the 10 batches studied, especially when part of a data set contained zeros and/or the numbers were low. The Negative Binomial fitted the laboratory batches best and the Poisson-Lognormal fitted the industrial batch best.