Modeling the inactivation of listeria monocytogenes by combined high pressure and temperature using weibull model

Inactivation curves of Listeria monocytogenes by high pressure were obtained at three pressure levels (400, 500 and 600 MPa) and three temperature levels (27, 43 and 60C) in ultra-high temperature (UHT) whole milk. The milk samples after treatment were plated on both nonselective and selective media to determine the log reduction value and to obtain the inactivation curve. The inactivation curves were fitted to the widely used two-parameter Weibull model with parameters α (characteristic time) and β (shape factor) and a reduced one-parameter Weibull model where the α value with the correct physical interpretation was predetermined. The log reduction value at the characteristic time from the regressed two-parameter Weibull model and the experimental data must both be 0.434; however, in the literature, there is evidence that the regressed model and the experimental values do not match always. Accordingly, this study focuses on the two-parameter and one-parameter Weibull models to bring out this inconsistency. Although there was loss in goodness of fit by adapting the one-parameter model, yet the model represented the correct physical interpretation of parameter α. Development of such mathematically consistent models may help industry to design, develop and optimize safe processing conditions that are based on reliable model parameters. Practical Application In previous studies, inactivation curves of microorganisms have been modeled using the widely used two-parameter Weibull model. However, it was not verified or investigated whether the parameters obtained by nonlinear regression represent the correct experimental value, especially the scale factor/characteristic time. The log reduction value obtained at a treatment time equals 5 to the regressed scale characteristic time should be 1/0.434 depending on the form of Weibull model used. However, in the literature, there is evidence that the regressed model and the experimental values do not match always. In this study, it was shown that predetermining the scale factor/characteristic time from the experimental data addresses this self-consistency issue. Development of such mathematically consistent models would help industry to design reliable and optimum safe processing conditions.