Mathematical description of non-linear survival curves of Listeria monocytogenes as determined in a beef gravy model system at 57.5 to 65 °C

Abstract

This paper presents a non-linear model for predicting the inactivation of Listeria monocytogenes, suspended in beef broth after heat treatment. A five-strain cocktail of L. monocytogenes was used in developing inactivation data at 57.5, 60, 62.5 and 65 °C, where maximum observed lethalities were more than 7 log 10 for the latter three temperatures. For all four temperatures, the survival curves, i.e. the common logarithms (base 10) of the numbers of surviving cells vs. times, were distinctly convex. Four functions, based on different assumptions underlying the shape of the survival curves, were compared. The assumptions involve the asymptotic behavior of the survival curves. Mechanistic considerations were used in deriving some of the functions considered. The function selected for further modeling was the logistic function, where the natural logarithm of time is the independent variable. Using this function, a model for predicting the amount of inactivation for temperatures between 57.5 and 65 °C was determined. The model presented in this paper is different from models that have been presented in the predictive microbiology literature, in that the parameters that describe the model are assumed to be random variables. Thus, a full description of the model includes standard deviations of parameter values, which were estimated using a mixed-effects analysis. Other research has indicated a logistic function adequately describes survival curves of L. monocytogenes. The use of this function entails that there are not non-zero asymptotic D-values. In conclusion, there is a substantial body of evidence suggesting that non-linear models are needed for characterizing survival curves of L. monocytogenes.