Development of a Predictive Mathematical Model for the Growth Kinetics of Listeria monocytogenes in Sesame Leaves

Square root models were developed for predicting the kinetics of growth of Listeria monocytogenes in sesame leaves as a function of temperature (4, 10, or $25^{\circ}C$). At these storage temperatures, the primary growth curves fit well ($R^2=0.898$ to 0.980) to a Gompertz equation to obtain lag time (LT) and specific growth rate (SGR). The square root models for natural logarithm transformations of the LT and SGR as a function of temperature were obtained by SAS's regression analysis. As storage temperature ($4-25^{\circ}C$) decreased, LT increased and SGR decreased, respectively. Square root models were identified as appropriate secondary models for LT and SGR on the basis of most statistical indices such as coefficient determination ($R^2=0.961$ for LT, 0.988 for SGR), mean square error (MSE=0.l97 for LT, 0.005 for SGR), and accuracy factor ($A_f=1.356$ for LT, 1.251 for SGR) although the model for LT was partially not appropriate as a secondary model due to the high value of bias factor ($B_f=1.572$). In general, our secondary model supported predictions of the effects of temperature on both LT and SGR for L. monocytogenes in sesame leaves.