An integral model of microbial inactivation taking into account memory effects: power-law memory kernel

In this article, we propose an alternative framework for the description of non-log-linear thermal inactivation of microorganisms. The proposed framework generalizes classical views by explicitly taking into account memory effects, such as those often associated with cumulative cell damage or progressive cell adaptation. Within this general framework, specialized memory models can be easily accommodated to describe different modes of microbial response to previous thermal stresses. In this introductory study, the advantages and limitations of the simplest nontrivial memory model, the power-law memory model, were explored. Our results indicate that for isothermal treatments the assumption of power-law memory leads to a simple solution that is known to describe a large number of non-log-linear survival curves. For nonisothermal treatments, the power-law memory model leads to predictions that agree well with experimental data. This research may lead to new insights into predictive microbiology with a new appreciation for the importance of memory effects.