Stability analysis of a bacterial growth model through computer algebra
Agustín G. Yabo1 ; Mohab Safey El Din2 ; Jean-Baptiste Caillau3 ; Jean-Luc Gouzé4
1 MISTEA, Université Montpellier, INRAE, Institut Agro, Montpellier, France
2 Sorbonne Université, LIP6 (UMR CNRS 7606), PolSys Team, France
3 Université Côte d’Azur, CNRS, Inria, LJAD, France
4 Université Côte d’Azur, Inria, INRAE, CNRS, Sorbonne Université, Biocore Team, Sophia Antipolis, France
MathematicS In Action, Tome 12 (2023) no. 1, pp. 175-189.

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.

Publié le :
DOI : 10.5802/msia.37
Classification : 37N25, 92-08, 13P15, 14Q30, 68W30
Mots clés : continuous bioreactors, self-replicator model, bacterial growth, local stability
Agustín G. Yabo 1 ; Mohab Safey El Din 2 ; Jean-Baptiste Caillau 3 ; Jean-Luc Gouzé 4

1 MISTEA, Université Montpellier, INRAE, Institut Agro, Montpellier, France
2 Sorbonne Université, LIP6 (UMR CNRS 7606), PolSys Team, France
3 Université Côte d’Azur, CNRS, Inria, LJAD, France
4 Université Côte d’Azur, Inria, INRAE, CNRS, Sorbonne Université, Biocore Team, Sophia Antipolis, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Agustín G. Yabo; Mohab Safey El Din; Jean-Baptiste Caillau; Jean-Luc Gouzé. Stability analysis of a bacterial growth model  through computer algebra. MathematicS In Action, Tome 12 (2023) no. 1, pp. 175-189. doi : 10.5802/msia.37. https://msia.centre-mersenne.org/articles/10.5802/msia.37/

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