When the Weibull model helps in deciphering bacterial resistance variability related to survival behaviour

Abstract

Survival curves of bacterial vegetative cells or spores subjected to an inactivation process are often log-linear and then described by the d-value parameter. However, non log-linear, convex, shapes might be also observed particularly when mild inactivation treatments are applied. Our objective was to investigate whether the 3-parameters Weibull model (logN₀, $\delta$, p) could be used to go beyond a simple fitting of convex curve by providing information related to bacterial variability. First, survival curves were simulated to mimic the behaviour of a cocktail containing bacterial vegetative cells or spores undergoing an inactivation treatment, on which the Weibull model was fitted. Second, a mathematical model was developed to describe the link between the Weibull parameters p and delta with the d-values of sub-populations of bacterial vegetative cells or spores (considering as well the percentage of each sub-population). Based on this model, it was shown that the Weibull model can be used to go beyond a simple description of a convex curve. For instance, if p is estimated around 0.8, that means the presence of a resistant sub-population, but with a limited resistant variability (ratio of resistance from 1.5 to 4). In contrast, if p is estimated to 0.3–04 that means the presence of a resistant sub-population in a small proportion (less than 10 %) combined with a large resistant variability (ratio of 10 or more). This study shows that the Weibull model can be used in combination with the new model developed here to decipher vegetative cell or spore resistance variability, with application in food industry processes such as thermal or physical inactivation treatment as well as cleaning and disinfection verification procedure.