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.

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Cells of Listeria monocytogenes or Salmonella enterica serovar Typhimurium taken from six characteristic stages of growth were subjected to an acidic stress (pH 3.3). As expected, the bacterial resistance increased from the end of the exponential phase to the late stationary phase. Moreover, the shapes of the survival curves gradually evolved as the physiological states of the cells changed. A new primary model, based on two mixed Weibull distributions of cell resistance, is proposed to describe the survival curves and the change in the pattern with the modifications of resistance of two assumed subpopulations. This model resulted from simplification of the first model proposed. These models were compared to the Whiting's model. The parameters of the proposed model were stable and showed consistent evolution according to the initial physiological state of the bacterial population. Compared to the Whiting's model, the proposed model allowed a better fit and more accurate estimation of the parameters. Finally, the parameters of the simplified model had biological significance, which facilitated their interpretation.When thermal or nonthermal inactivation of spores or vegetative microorganisms is considered, the log-linear shape of bacterial survival curves is a particular case among types of curves (12,17,43,49). In the case of nonthermal inactivation caused by unfavorable environmental conditions, the shape of curves indicates more pronounced heterogeneity according to the intensity of the stress. A bacterial strain can produce different shapes of survival curves. Frequently, concave curves may become convex or sigmoidal when the intensity of the stress varies (6,7,10,19,24,38,45,47,48). The patterns of survival curves may also vary with the physiological state of the cells and are dependent on the phase of growth (exponential or stationary phase) and also on the conditions of adaptation before the stress (18,25,36).In order to model nonthermal inactivation curves, a number of primary models have been proposed. Among these models are the vitalistic models proposed by Cole et al. (13,28,39), models describing both growth and inactivation (26,27,32,37,40,41), the modified Gompertz model (24, 32), the exponential model (31), and the log-linear model with latency time (6) and/or with a tail (5). These models cannot deal with all shapes of curves, and most of them are based on log-linear inactivation.Some models can describe non-log-linear decrease or sigmoidal inactivation curves. The Weibull model has largely been used in thermal and nonthermal treatment studies. It is based on the hypothesis that the resistance to stress of a population follows a Weibull distribution (14,19,34,44,45). This type of model can describe linear, concave, or convex curves. It was modified and extended to sigmoidal curves in heat treatment studies (2). The model of Baranyi and Roberts (3) and the model of Geeraerd et al. (17) can describe a linear shape with or without shoulder or tail and sigmoidal shapes (21,22). These models, which can...

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.