Predictive Microbiology in Foods by Fernando Perez-Rodriguez & Antonio Valero

Author:Fernando Perez-Rodriguez & Antonio Valero
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(4.16)

where f(t) i represents an adaptation function and α(t) i is an inhibition function for a population i.

Cornu et al. (2002, 2011) incorporated the Jameson effect hypothesis into a growth model, assuming that the inhibition effect is equal for all competitive microbial populations, thus α(t) I is an inhibition function so that , being a modification of the logistic function of deceleration, is based on the densities of both populations and written as follows:

(4.17)

This inhibition function has been modified by other authors to explain the effect of specific bacterial populations in determined food matrices (Le Marc et al. 2009; Mejlholm and Dalgaard 2007).

The interaction models based on the Lotka–Volterra type models can be considered as a variation of the previous mathematical structure in which there exist as many functions f(t) as potential competitive microbial populations in which each population has a different inhibition effect represented by the coefficient in the following general equation (Vereecken et al. 2000; Vereecken and Van Impe 2002; Powell 2004):

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