On the use of the Weibull model to describe thermal inactivation of microbial vegetative cells

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This paper evaluates the applicability of the Weibull model to describe thermal inactivation of microbial vegetative cells as an alternative for the classical Bigelow model of first-order kinetics; spores are excluded in this article because of the complications arising due to the activation of dormant spores. The Weibull model takes biological variation, with respect to thermal inactivation, into account and is basically a statistical model of distribution of inactivation times. The model used has two parameters, the scale parameter alpha (time) and the dimensionless shape parameter beta. The model conveniently accounts for the frequently observed nonlinearity of semilogarithmic survivor curves, and the classical first-order approach is a special case of the Weibull model. The shape parameter accounts for upward concavity of a survival curve (beta <1), a linear survival curve (beta = 1), and downward concavity (beta > 1). Although the Weibull model is of an empirical nature, a link can be made with physiological effects. beta <1 indicates that the remaining cells have the ability to adapt to the applied stress, whereas beta > 1 indicates that the remaining cells become increasingly damaged. Fifty-five case studies taken from the literature were analyzed to study the temperature dependence of the two parameters. The logarithm of the scale parameter a depended linearly on temperature, analogous to the classical D value. However, the temperature dependence of the shape parameter beta was not so clear. In only seven cases, the shape parameter seemed to depend on temperature, in a linear way. In all other cases, no statistically significant (linear) relation with temperature could be found. In 39 cases, the shape parameter beta was larger than 1, and in 14 cases, smaller than 1. Only in two cases was the shape parameter b = 1 over the temperature range studied, indicating that the classical first-order kinetics approach is the exception rather than the rule. The conclusion is that the Weibull model can be used to model nonlinear survival curves, and may be helpful to pinpoint relevant physiological effects caused by heating. Most importantly, process calculations show that large discrepancies can be found between the classical first-order approach and the Weibull model. This case study suggests that the Weibull model performs much better than the classical inactivation model and can be of much value in modelling thermal inactivation more realistically, and therefore, in improving food safety and quality. (C) 2002 Elsevier Science B.V. All rights reserved.
Original languageEnglish
Pages (from-to)139-159
JournalInternational Journal of Food Microbiology
Issue number1-2
Publication statusPublished - 2002


  • log-logistic model
  • listeria-monocytogenes
  • heat-resistance
  • survival curves
  • yersinia-enterocolitica
  • salmonella-enteritidis
  • predictive models
  • bovine-milk
  • temperature
  • kinetics


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