Differential equations system to describe bacterial growth, pH variation and lactic acid production in batch fermentation

Resumen

A mathematical model composed of a set of first order
ordinary differential equations is proposed for describing
the dynamics between biomass concentration, pH variation,
and lactic acid production by a strain of lactic acid bacteria
(LAB) during fermentation process under specific culture
conditions to produce jocoque-type fermented milk. The
mathematical model was built using a modeling software
called Eureqa and was formulated from experimental data
obtained from batch fermentation of 10% milk powder
incubated at temperature of 37 ° C for 48 hours. The
solutions of the mathematical model describe information
obtained by experimental data with a coefficient of
determination (R2) of 0.90 for biomass, 0.97 for pH and 0.92
for acidity production. The theory of positivity of non-linear
systems and the localization of compact invariant sets
method were applied to analyze the global dynamics of the
system and determine its lower and upper bounds,
additionally its equilibrium points and eigenvalues were
calculated to determine results that are biologically feasible
and asymptotically stable. In this way, it is expected that the
model will become a support tool for the standardization of
fermented milk production and that the prediction of the
behavior of these variables will ensure the quality of
fermented milk products.