Empirical model building based on Weibull distribution to describe the joint effect of pH and temperature on the thermal resistance of Bacillus cereus in vegetable substrate

A mathematical model based on Weibull parameters was built to describe the joint effect of temperature and pH on thermal inactivation of Bacillus cereus spores (strain INRA TZ415). The effect of these factors on Weibull model parameters ( β, 1/ α) was also studied. Heat inactivation tests were carried out in acidified carrot broth as vegetable substrate, following a full factorial design at four levels for temperature (80, 85, 90 and 95 °C) and pH (6.2, 5.8, 5.2 and 4.7). The Weibull distribution model provided good individual fits for the different combinations of temperature–pH tested, with discrepancy factors, D f, coming close to 25% for most cases. The temperature and pH did not have a significant effect on the shape parameter ( β), which yielded a mean value of 0.88. The scale parameter ( α) decreased with pH, and its inverse (1/ α) followed an Arrhenius-type relationship with temperature. A global model was built, including the dependence of the α parameter on temperature and pH, and the model parameters were estimated by using a one-step nonlinear least-squares regression to improve the precision of the estimates. Results indicated that the global model provides a satisfactory description of the thermal inactivation of B. cereus spores, with R 2 equal to 0.983.