Mathematical Modeling for Fermentation Systems: A Case Study in Probiotic Beer Production

The use of autochthonous yeast strains from viticultural environments represents a novel approach in the brewing industry. Probiotic-fermented beers have generated growing interest as they combine traditional brewing with the increasing demand for health-oriented functional beverages. The application of mathematical modeling to fermentation kinetics becomes a crucial tool to adequately describe and subsequently improve the performance of functional beer fermentation. The Saccharomyces cerevisiae PB101 autochthonous yeast from San Juan (Argentina) was previously selected for its probiotic potential and its exceptional technological traits in beer wort production. It was subsequently used to ferment a K & ouml;lsch-style brewer's wort in order to evaluate both its probiotic potential and its resistance to the human digestive system. The results showed a survival percentage of 73.49 +/- 0.54 and 80.17 +/- 3.73 in fermentations conducted in 2024 and 2025, respectively. These fermentation assays were used to explore kinetic microbial growth, ethanol production, and critical fermentation parameters. Traditional modeling approaches often fail to adequately capture the intricacies of probiotic fermentations, particularly lag phases associated with microbial adaptation and metabolite biosynthesis. To address these limitations, this study develops an innovative and simple modeling system for modeling probiotic beer fermentation by incorporating two state variables: total and dead cells. The dynamics of these two variables were modeled using either a First Order Plus Dead Time model or a logistic growth model. Furthermore, the modified Luedeking-Piret model was used to study the delay time that exists between the production of viable cells and ethanol. The proposed models demonstrate enhanced predictive accuracy and dependability, providing a solid foundation for optimizing fermentation processes and advancing the development of functional beverages with exceptional probiotic properties.