Predicting the Shelf Life of Dairy Products through Mathematical Modelling and in silico Experimentation

Yolocuauhtli Salazar-Muñoz; Paul A. Valle; Emmanuel Rodríguez; Manuel F. Alvarado Ontíveros

doi:10.17488/RMIB.45.2.6

Authors

Yolocuauhtli Salazar-Muñoz Tecnológico Nacional de México/Instituto Tecnológico de Durango, México https://orcid.org/0000-0002-5563-2692
Paul A. Valle Tecnológico Nacional de México/Instituto Tecnológico de Tijuana, México https://orcid.org/0000-0001-6567-1065
Emmanuel Rodríguez Tecnológico Nacional de México/Instituto Tecnológico de Tijuana, México https://orcid.org/0000-0003-4781-5138
Manuel F. Alvarado Ontíveros Tecnológico Nacional de México/Instituto Tecnológico de Durango, México https://orcid.org/0009-0007-7900-9938

DOI:

https://doi.org/10.17488/RMIB.45.2.6

Keywords:

experimental data, nonlinear regression, nonlinear time-varying systems, numerical simulations, shelf life

Abstract

The preservation of foods such as milk, meat, and vegetables through fermentation results in products like yogurt, cheese, pickles, sausages, and silage with an extended shelf life compared to their natural unprocessed counterparts. This work aims to formulate a mathematical model of first-order ordinary differential equations (ODEs) that accounts for both the physicochemical and microbiological parameters affecting biomass kinetics [B(t)], acidity [A(t)], and viscosity [V(t)] as a function of temperature across different yogurt samples. In order to validate the efficacy of the model in predicting yogurt shelf life, we compared its fitting results with commonly employed systems or equations, including the Weibull model, the Reaction Order model, the Arrhenius Equation, and the Q10 Factor. Our evaluation, based on R-squared (R²) values exceeding 0.95, demonstrates the robustness of the proposed model. Furthermore, all parameters were estimated along with their corresponding 95 % confidence intervals. The mathematical model estimates the dynamic of each of the physicochemical and microbiological parameters which will help to predict the behavior over time of the shelf life of yogurt at different temperatures.

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