Developing a full Weibull model for microbial survival during food processing

Microbial survival models play a key role in food process calculations and control to ensure the microbiological safety of processed foods. In this study, a full Weibull model was developed to describe monophasic microbial survival curves that exhibit both a shoulder and a tail. It was demonstrated that the model encompasses the modified Gompertz model and the log-logistic model, which are frequently used to describe survival curves with a should and/or a tail. Due to the simple mathematical structure of the full Weibull model, its integral representation was derived to conveniently calculate survival curves under a non-constant condition. Furthermore, under a constant condition with come-up time (CUT), the integral equation was converted into an algebraic equation that involves CUT and log₁₀S_CUT. Results showed survival parameters could be accurately estimated by fitting the algebraic equation to survival curves under constant conditions with CUT.