Microbiological risk assessment models for partitioning and mixing during food handling

To describe the transmission dynamics of a pathogen over a food pathway in quantitative microbiological risk assessment (QMRA), several types of processes need to be modelled. Next to microbial processes like bacterial growth and inactivation, four food handling processes can be identified. Among these are partitioning and mixing of the food product. With these processes, the (sizes of) units of food product are modified and the pathogenic cells are reallocated over the units, so that the prevalence of contaminated units and the number of cells per unit may change. Usually, simple models of these processes are applied in QMRA food chain models. These models assume independence of units, random homogeneous distribution of cells (for partitioning) and equal contribution of units (for mixing), which is often not realistic in food and food handling processes. In this paper, these assumptions are abandoned. The use of multivariate distributions is proposed to include the effect of dependence between units: the Multinomial distribution for partitioning and the Dirichlet distribution for mixing. Effects of cell clustering and/or unequal sizes of units formed by partitioning or contributing to mixing are incorporated. Some algorithms are derived that are easily implemented in spreadsheet models that simulate food production and preparation. Some examples show the effect of more realistic modelling by implementation of these algorithms on the prevalence and the probability distribution of the number of pathogens per unit of food product. In general, cell clustering will result in lower prevalences, but higher levels of contamination in contaminated food units. With the methods presented, these effects can be quantified. Difficulties in estimating the model parameters and the impact of implementation of the proposed methods on risk estimates in QMRA are discussed.