Modeling inactivation of Listeria monocytogenes using Weibull model under combined effect of high pressure and temperature in whole milk

Abstract

Survival curves for Listeria monocytogenes were obtained at seven combinations of pressure and temperatures. Both Log linear and a two-parameter Weibull equations were used to model the survival curves. Based on the goodness of fit analysis (R2 and MSE values), the Weibull model was deemed to more accurately represent the survival data. The Weibull model parameters a (characteristic time) and s (shape factor) were determined. Additionally, the reliable life (tR) was calculated using a and s; which is equal to the decimal reduction time (D-value) when s = 1. Although the two parameters of Weibull model seemed to fit the inactivation data well; however, further analysis showed that the a value obtained from the non-linear regression-based model did not fit the correct physical interpretation of parameter a. According to the definition of a, it represents a characteristics time for which the log reduction value is 0.434. In other words, when a is equal to the treatment time, the log reduction value obtained by Weibull model should equal 0.434. But from the observed data when the treatment time for 0.434 log10 reduction was calculated it was not matching the a value obtained by non-linear regression. Therefore, an attempt was made to fit the Weibull model with correct interpretation of a. For this, the treatment time for 0.434 log10 reduction was calculated by linear interpolation from the first two experimental treatment times and that value was taken as a. In other word, the value of a was constrained in the model and regression was run to determine the best value of s. By adopting this approach, a trend for values of a and s with temperature and pressure was found; whereas, the parameters values obtained without constraining a did not show a trend with pressure and temperature.