Castillo, Aurelio

Rodriguez, Emmanuel

Salazar, Yolocuauhtli

Valle, Paul A.

English

ISU ReD: Research and eData

Presentation for the Symposium on BEER November 2020Dynamic between biomass, pH and acid lactic bymicroorganisms in fermentation of fresh milkEmmanuel Rodŕıguez1,*, Aurelio Castillo1, Paul A. Valle2, Yolocuauhtli Salazar11Tecnológico Nacional de México , IT Durango. Maestŕıa en Ingenieŕıa2Tecnológico Nacional de México , IT Tijuana. Posgrado en Ciencias de la Ingenieŕıa, grupo de InvestigaciónBioMath10040780@itdurango.edu.mxIn this research a mathematical model composed by a set of Ordinary Differential Equations (ODEs) isformulated in order to describe the dynamics between biomass concentration (UFC), pH variation and acidlactic (aL) produced by a strain of microorganisms during a batch fermentation of fresh milk under specificculture conditions. Our mathematical model was constructed with a modelling software called Eureqa, itwas based on the logistic equation, the law of mass action and some biological suppositions. The designconsidered that all three populations do not grow exponentially, they must have biological feasible limits andare described by non-negative numbers, biomass tends to zero at large time if and only if the medium is notcontaminated and the temperature is constant. Positivity of the system was verified through the Leenheerand Aeyels theorem to determine positivity for non-linear systems. In order to analyze its global dynamics,the method of compact invariant sets proposed by Krishchenko was applied to calculate upper and lowerbounds of the localizing domain. Further, the structure and dynamics of the proposed model is consistentwith the literature regarding behavior of its solutions. Therefore, it is expected that the ODE system willbecome a support tool for standardization of fermented milk production as well as the behavior predictionof variables (UFC, pH, aL) will ensure the quality of fermented milk products. Further research is focusedto carry out the analysis of existence and uniqueness, moreover establish a control variable that allows tobring the system to a desired state.

Dynamic Between Biomass, pH and Acid Lactic by Microorganisms in Fermentation of Fresh Milk

https://ir.library.illinoisstate.edu/cgi/viewcontent.cgi?filename=0&article=1467&context=beer&type=additional

Dynamic Between Biomass, pH and Acid Lactic by Microorganisms in Fermentation of Fresh Milk

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ISU ReD: Research and eData