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
alpha 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 beta = 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.