Mathematical modeling of growth of Salmonella in raw ground beef under isothermal conditions from 10 to 45 °C

The objective of this study was to develop primary and secondary models to describe the growth of Salmonella in raw ground beef. Primary and secondary models can be integrated into a dynamic model that can predict the microbial growth under varying environmental conditions. Growth data of Salmonella at nine different isothermal conditions — 10, 15, 20, 25, 28, 32, 35, 42, and 45 °C were first fitted into primary models, namely the logistic, modified Gompertz, Baranyi, and Huang models. Performances of these models were evaluated by using various statistical criteria, namely mean square error (MSE), pseudo-R2, − 2 log likelihood, Akaikeʹs and Bayesianʹs information criteria. All the chosen models fitted well to the growth data of Salmonella based on these criteria. The results of statistical analysis showed that there was no significant difference in the performances of the four primary models, suggesting that the models were equally suitable for describing isothermal bacterial growth. The specific growth rates derived from each model was fitted to the Modified Ratkowsky equation, relating the specific growth rate to growth temperatures. It was also observed that the lag phase duration was an inverse function of specific growth rates. These models, if validated, can be used to construct dynamic models to predict potential Salmonella growth in raw ground beef.