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Updated: Jul 30, 2026

The Use of Chemostats in Microbial Systems Biology
Published on: October 14, 2013
A size-structured, non-conservative ODE model of the chemostat
1Department of Mathematics and Statistics, University of Victoria, Victoria BC, Canada V8W 3P4. jarino@math.uvic.ca
Abstract:
We study a class of size-structured, ODE models of growth in the chemostat, that take into account cell maintenance and substrate dependent cell mortality. Unlike most classical chemostat models, they are supposed to be non-conservative, in the sense that they do not verify the mass conservation principle. However, using a change of time scale, we are able to obtain qualitative results. Then, using a Lyapunov functional, we prove the global stability of the non-trivial equilibrium. Some examples of the possible structure of the models are given to finish with.
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