Open AccessA nonautonomous chemostat model for the growth of gut microbiome with varying nutrient
Author(s) -
Brittni Hall,
Xiaoying Han,
Peter E. Kloeden,
HansWerner van Wyk
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022075
Subject(s) - chemostat , pullback attractor , gut microbiome , attractor , stability (learning theory) , mathematics , biological system , microbiome , mechanics , control theory (sociology) , mathematical analysis , physics , biology , computer science , bioinformatics , artificial intelligence , genetics , control (management) , machine learning , bacteria
A mathematical model describing the growth of gut microbiome inside and on the wall of the gut is developed based on the chemostat model with wall growth. Both the concentration and flow rate of the nutrient input are time-dependent, which results in a system of non-autonomous differential equations. First the stability of each meaningful equilibrium is studied for the autonomous counterpart. Then the existence of pullback attractors and its detailed structures for the nonautonomous system are investigated using theory and techniques of nonautonomous dynamical systems. In particular, sufficient conditions under which the microbiome vanishes or persists are constructed. Numerical simulations are provided to illustrate the theoretical results.