Characteristics of the Stochastic and Kinetic Models to Thermal Death of Microbes in Food

The characteristics of stochastic and kinetic models were studied on description of the survivor curve of microbes in food during heating. Exponential and Weibull distributions were used in the stochastic models to model the lifetime of cells and exponential and Weibull functions were used in the kinetic models to model the number of survivors. The data were random samples generated from exponential and Weibull distributions, which can be thought to be the lifetimes of microbial cells heated at a given temperature, and microbial survivor data imaginarily produced from previous papers. The stochastic and kinetic models were fit to data with the maximum likelihood method and the least squares method, respectively. Both models successfully described the survivor curves of random sampling data originated from exponential and Weibull distributions. Namely, both models precisely described linear survivor curves and no-linear ones having an upward concave or a shoulder. For microbial data, the kinetics models precisely described a linear and non-linear curve, while the stochastic models precisely described the survivors at early times of heating, but not those at later times. Similar results on the two models were observed in other survivor data as well. The kinetic models showed better performance in fitting the whole survivor curves than the stochastic ones under the present modeling and estimation frameworks.