Describing the Individual Spore Variability and the Parameter Uncertainty in Bacterial Survival Kinetics Model by Using Second-Order Monte Carlo Simulation

The objective of this study was to separately describe the fitting uncertainty and the variability of individual cell in bacterial survival kinetics during isothermal and non-isothermal thermal processing. The model describing bacterial survival behavior and its uncertainties and variabilities during non-isothermal inactivation was developed from survival kinetic data for Bacillus simplex spores under fifteen isothermal conditions. The fitting uncertainties in the parameters used in the primary Weibull model was described by using the bootstrap method. The variability of individual cells in thermotolerance and the true randomness in the number of dead cells were described by using the Markov chain Monte Carlo (MCMC) method. A second-order Monte Carlo (2DMC) model was developed by combining both the uncertainties and variabilities. The 2DMC model was compared with reduction behavior under three non-isothermal profiles for model validation. The bacterial death estimations were validated using experimentally observed surviving bacterial count data. The fitting uncertainties in the primary Weibull model parameters, the individual thermotolerance heterogeneity, and the true randomness of inactivated spore counts were successfully described under all the iso-thermal conditions. Furthermore, the 2DMC model successfully described the variances in the surviving bacterial counts during thermal inactivation for all three non-isothermal profiles. As a template for risk-based process designs, the proposed 2DMC simulation approach, which considers both uncertainty and variability, can facilitate the selection of appropriate thermal processing conditions ensuring both food safety and quality.