Development of a dynamic continuous-discrete-continuous model describing the lag phase of individual bacterial cells

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Abstract
Aims: A previous model for adaptation and growth of individual bacterial cells was not dynamic in the lag phase, and could not be used to perform simulations of growth under non‐isothermal conditions. The aim of the present study was to advance this model by adding a continuous adaptation step, prior to the discrete step, to form a continuous‐discrete‐continuous (CDC) model. Methods and Results: The revised model uses four parameters: N0, intial population; Nmax, maximum population; p0, mean initial individual cell physiological state; SDp0, standard deviation of the distribution of individual physiological states. A truncated normal distribution was used to generate tables of distributions to allow fitting of the CDC model to viable count data for Listeria monocytogenes grown at 5°C to 35°C. The p0 values increased with increasing SDp0 and were, on average, greater than the corresponding population physiological states (h0); p0 and h0 were equivalent for individual cells. Conclusions: The CDC model has improved the ability to simulate the behaviour of individual bacterial cells by using a physiological state parameter and a distribution function to handle inter‐cell variability. The stages of development of this model indicate the importance of physiological state parameters over the population lag concept, and provide a potential approach for making growth models more mechanistic by incorporating actual physiological events. Significance and Impact of the Study: Individual cell behaviour is important in modelling bacterial growth in foods. The CDC model provides a means of improving existing growth models, and increases the value of mathematical modelling to the food industry.