A stochastic approach for modelling the effects of temperature on the growth rate of Bacillus cereus sensu lato

Yvan Le Marc*, Nathália Buss da Silva, Florence Postollec, Véronique Huchet, József Baranyi, Mariem Ellouze

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)


A stochastic model that predicts the maximum specific growth rate (μmax) of Bacillus cereus sensu lato as a function of temperature was developed. The model integrates the intra-species variability by incorporating distributions of cardinal parameters (Tmin, Topt, Tmax) in the model. Growth rate data were generated for 22 strains, covering 5 major phylogenetic groups of B. cereus, and their cardinal temperatures identified. Published growth rate data were also incorporated in the model fitting, resulting in a set of 33 strains. Based on their cardinal temperatures, we identified clusters of Bacillus cereus strains that show similar response to temperature and these clusters were considered separately in the stochastic model. Interestingly, the μopt values for psychrotrophic strains were found to be significantly lower than those obtained for mesophilic strains. The model developed within this work takes into account some correlations existing between parameters (μopt, Tmin, Topt, Tmax). In particular, the relationship highlighted between the b-slope of the Ratkowsky model and Tmin (doi: https://doi.org/10.3389/fmicb.2017.01890) was adapted to the case of the popular Cardinal Temperature Model. This resulted in a reduced model in which μopt is replaced by a function of Tmin, Topt and 2 strain-independent parameters. A correlation between the Tmin parameter and the experimental minimal growth temperature was also highlighted and integrated in the model for improved predictions near the temperature growth limits. Compared to the classical approach, the model developed in this study leads to improved predictions for temperatures around Tmin and more realistic tails for the predicted distributions of μmax. It can be useful for describing the variability of the Bacillus cereus Group in Quantitative Microbial Risk Assessment (QMRA). An example of application of the stochastic model to Reconstituted Infant Formulae (RIF) was proposed.

Original languageEnglish
Article number109241
JournalInternational Journal of Food Microbiology
Publication statusPublished - 2 Jul 2021


  • Bacillus cereus
  • Cardinal temperatures
  • Microbial risk assessment
  • Stochastic model
  • Tertiary modelling


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