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J Appl Microbiol. 2001 Mar;90(3):407-13.

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

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Food Research Program, Southern Crop Protection and Food Research Centre, Agriculture and Agri-Food Canada, Guelph, Ontario, Canada.



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.


The revised model uses four parameters: N(0), initial population; N(max), maximum population; p0, mean initial individual cell physiological state; SD(p0), 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 degrees C to 35 degrees C. The p0 values increased with increasing SD(p0) and were, on average, greater than the corresponding population physiological states (h0); p0 and h0 were equivalent for individual cells.


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.


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.

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