Modeling the growth kinetics of Bacillus cereus as a function of temperature, pH, sodium lactate and sodium chloride concentrations

Mathematical models describing the growth kinetic parameters (lag phase duration and growth rate) of Bacillus cereus as a function of temperature, pH, sodium lactate and sodium chloride concentrations were obtained in this study. In order to get a residual distribution closer to a normal distribution, the natural logarithm of the growth kinetic parameters were used in modeling. For reasons of parsimony, the polynomial models were reduced to contain only the coefficients significant at a level of p≤0.05. Using the reduced polynomial models ( R 2 of 95.2% and 93.9% for ln LAG and ln GR models, respectively), three-dimensional graphs were drawn illustrating the effects of the independent variables on the growth parameters. Predicted data were compared with the predictions from Pathogen Modeling Program (PMP—US Department of Agriculture–Agricultural Research Service) and validated against data extracted from the literature. The mean absolute relative error (MARE) and the median relative error (MRE) of the predicted generation times with the derived model were 25.6% and −16.7%, respectively, showing that the growth rate model accurately and safely predicted the growth kinetics of B. cereus. Results of the modeling study indicated that all of the studied factors had a significant effect on the growth of B. cereus in the experimental range studied.