Summary: A size-structured, non-conservative ODE model
of the chemostat
Julien Arino a,*, Jean-Luc Gouzee b
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4
Comore Research Project, INRIA Sophia Antipolis, BP 93, 06902 Sophia Antipolis cedex, France
Received 15 December 2000; received in revised form 19 November 2001; accepted 15 December 2001
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. Ó 2002 Elsevier Science Inc. All rights reserved.
Keywords: Chemostat; Size-structured models; Non-conservative models; Cellular death; Maintenance
Consider the classical two-dimensional Monod model