Bayesian statistical modeling to describe uncertainty of thermal inactivation behaviour of bacterial spores

Abstract

To produce high-quality ready-to-eat food, excessive heat treatment must be avoided to maintain product quality. However, there is a risk of survival of heat-tolerant bacterial spores, such as those of Bacillus simplex. Therefore, the thermal inactivation process needs optimization, considering the product's properties, such as pH, and water activity (aw). This study aimed to develop a thermal inactivation prediction model for B. simplex as a function of heating temperature, pH, and aw, which expresses the uncertainty of the prediction error as a probability distribution using Bayesian inference. The survival kinetics of B. simplex spores were successfully fitted using the Weibull model, and the number of surviving B. simplex spores was estimated as a probability distribution, where the parameters were described as a function of heating temperature, pH, and aw using Bayesian regression. The B. simplex survival kinetics was successfully described as a 95% prediction band by using the estimated parameter distribution, and 84% of the validation data from bacterial culture agreed with the 95% prediction band. Although validation with real food, such as meat sauce, demonstrated that the predictive model is valid, it was not valid for other fat- or sugar-rich sauces, such as carbonara and Japanese cooked beef stew. These facts suggest that environmental factors other than temperature, pH, and aw should be incorporated into the secondary model. Nevertheless, the prediction of B. simplex survival with uncertainty using a combination of multiple environmental factors would enable a more accurate and realistic evaluation of the optimal thermal inactivation conditions.