Waltman 9801622 The chemostat (also called a continuous culture or a bioreactor) is a basic model of an open system. It is a model of a simple lake, a laboratory version of the commercial bio-reactor, and the starting point for models of waste water treatment and models of the mammalian intestine. Microorganisms compete for an input nutrient in an exploitative manner. The equations governing the model take the form of systems of nonlinear ordinary or partial differential equations. In this project, the investigator adds new features to the basic model in order to make it more realistic. This complicates the equations and hence the mathematical analysis. Specifically, the effects of wall growth, diffusion, transport, inhibitors (natural and external), and plasmid dynamics on the outcome of the competition are to be studied. The goal of the mathematical analysis is to identify the global asymptotic behavior of the solutions to these equations in terms of the system parameters (measurable or operational parameters). Inhibitors occur naturally (for example, anti-competitor toxins) or as pollutants. Growth of microorganisms on the wall (or other surface) can impede the efficiency of a biochemical reactor or contaminate any flow process. The asymptotic analysis of such problems can lead to a better understanding of natural phenomena or of reactor technology. Knowledge of this behavior allows one to predict the outcome of a fixed (i.e., natural) environment or to control the outcome in the case of an artificial (commercial) environment. All of the effects mentioned above come together is models of the mammalian intestine where wall growth is essential to the process, inhibitors affect the competition and where transport and diffusion cannot be ignored. One of the objectives of the study is to provide a better model of the human large intestine and a better understanding of the relative effect of each of the phenomena involved.
