Heat activates the dormant spores of certain Bacillus spp., which is reflected in the "activation shoulder" in their survival curves. At the same time, heat also inactivates the already active and just activated spores, as well as those still dormant. A stochastic model based on progressively changing probabilities of activation and inactivation can describe this phenomenon. The model is presented in a fully probabilistic discrete form for individual and small groups of spores and as a semicontinuous deterministic model for large spore populations. The same underlying algorithm applies to both isothermal and dynamic heat treatments. Its construction does not require the assumption of the activation and inactivation kinetics or knowledge of their biophysical and biochemical mechanisms. A simplified version of the semicontinuous model was used to simulate survival curves with the activation shoulder that are reminiscent of experimental curves reported in the literature. The model is not intended to replace current models to predict dynamic inactivation but only to offer a conceptual alternative to their interpretation. Nevertheless, by linking the survival curve's shape to probabilities of events at the individual spore level, the model explains, and can be used to simulate, the irregular activation and survival patterns of individual and small groups of spores, which might be involved in food poisoning and spoilage. Copyright © 2010, American Society for Microbiology. All Rights Reserved.
Corradini, M. G., Normand, M. D., Eisenberg, M., & Peleg, M. (2010). Evaluation of a stochastic inactivation model for heat-activated spores of bacillus spp. Applied and Environmental Microbiology, 76(13), 4402–4412. https://doi.org/10.1128/AEM.02976-09