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Stability analysis of a bacterial growth model through computer algebra

Agustín Gabriel Yabo 1, 2, 3 Mohab Safey El Din 4 Jean-Baptiste Caillau 2, 5, 3 Jean-Luc Gouzé 1 
1 BIOCORE - Biological control of artificial ecosystems
CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche, INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
2 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We describe microbial growth and production of value-added chemical compounds in a continuous bioreactor through a dynamical system and we study the local stability of the equilibrium of interest by means of the classical Routh-Hurwitz criterion. The mathematical model considers various biological and structural parameters related to the bioprocess (concentration of substrate inflow, constants of the microchemical reactions, steady-state mass fractions of intracellular proteins, etc.) and thus, the stability condition is given in terms of these parameters. This boils down to deciding the consistency of a system of polynomial inequalities over the reals, which is challenging to solve from an analytical perspective, and out of reach even for traditional computational software designed to solve such problems. We show how to adapt classical techniques for solving polynomial systems to cope with this problem within a few minutes by leveraging its structural properties, thus completing the stability analysis of our model. The paper is accompanied by a Maple worksheet available online.
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https://hal.archives-ouvertes.fr/hal-03671432
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Submitted on : Wednesday, May 18, 2022 - 1:20:15 PM
Last modification on : Friday, August 5, 2022 - 3:50:27 AM

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  • HAL Id : hal-03671432, version 1

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Agustín Gabriel Yabo, Mohab Safey El Din, Jean-Baptiste Caillau, Jean-Luc Gouzé. Stability analysis of a bacterial growth model through computer algebra. 2022. ⟨hal-03671432⟩

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