A simple and parsimonious model which originated from the Weibull frequency distribution was proposed to describe nonlinear survival curves of spores. This model was suitable for downward concavity curves (Bacillus cereus and Bacillus pumilus), as well as for upward concavity curves (Clostridium botulinum). It was shown that traditional F values calculated from this new model were no longer additive, to such an extent that a heat treatment should be better characterized by the obtained decimal reduction of spores. A modified Bigelow method was then proposed to assess this decade reduction or to optimize the heat treatment for a target reduction ratio.

Cytotoxic activity levels of culture filtrates and toxin distributions varied according to the phylogenetic group (I to VII) within the Bacillus cereus group, suggesting that these groups are of different clinical significance and are more suitable than species affiliations for determining food poisoning risk. A first-line, simple online tool (https://www.tools.symprevius.org/Bcereus/english.php) to assign strains to the different phylogenetic groups is presented.

The classical D-value of first order inactivation kinetic is not suitable for quantifying bacterial heat resistance for non-log linear survival curves. One simple model derived from the Weibull cumulative function describes non-log linear kinetics of micro-organisms. The influences of environmental factors on Weibull model parameters, shape parameter "p" and scale parameter "delta", were studied. This paper points out structural correlation between these two parameters. The environmental heating and recovery conditions do not present clear and regular influence on the shape the parameter "p" and could not be described by any model tried. Conversely, the scale parameter "delta" depends on heating temperature and heating and recovery medium pH. The models established to quantify these influences on the classical "D" values could be applied to this parameter "delta". The slight influence of the shape parameter p variation on the goodness of fit of these models can be neglected and the simplified Weibull model with a constant p-value for given microbial population can be applied for canning process calculations.

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