Abstract
Three most commonly used primary models (Gompertz, Baranyi and three-phase linear models) to describe the microbial growth curves were applied to three different isothermal growth data of Listeria monocytogenes. Further Monte Carlo analysis was performed with 100, 1000 and 10000 simulations. The results indicated that there was no reason to use higher number of simulations since the simulations produced almost identical means of the model parameter values for all models. Moreover, the models had similar coefficient of variation values for the initial (log10N0) and maximum (log10Nmax) number of bacteria. On the other hand, the Gompertz model had the highest coefficient of variation for the growth rate (µmax) and the Baranyi model had the highest coefficient of variation for the lag time (λ). Correlations between the parameters log10N0 and λ, and µmax and λ could be easily observed after the Monte Carlo analysis for all models. Deviation from normal distribution for the parameter λ for the three-phase linear model was evident, other than that all parameters for all models had normal distribution. It was concluded that Monte Carlo analysis can be used as a simple yet an effective method to describe the uncertainty in model parameters and correlation between the parameters as well as the spread of the possible parameter values.
Highlights
Mathematical models have been used to evaluate microbial behavior such as inactivation, survival or growth under different environmental conditions (Gwak et al, 2015)
For the data set of McKellar (1997) the Baranyi model was again the best model followed by the Gompertz and the three phase linear models (Table S2)
We have shown the same result by using Monte Carlo (MC) analysis with three different data sets including the three-phase linear model
Summary
Mathematical models have been used to evaluate microbial behavior such as inactivation, survival or growth under different environmental conditions (Gwak et al, 2015). Monte Carlo (MC) analysis is based on random computer simulations of the experimental data which are described by a mathematical model It is most probably the simplest and the best analysis to describe the uncertainty in model parameters (van Boekel, 2009). The usage of MC in the field of predictive microbiology can be found in literature (Abe et al, 2019; Cassin et al, 1998; Coleman and Marks, 1999; Koyama et al, 2019; Nauta, 2000; Nicolaï and Van Impe, 1996) It was used for primary growth models such as Baranyi model (Poschet et al, 2004; 2003) and Gompertz model (Lambert et al, 2012). Further objective was to make comparisons between the models based on the results of MC simulations such as correlations of the model parameters
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