Waltman The investigator develops and analyzes a class of biological models generally described as chemostat-like models. While ordinary differential equations techniques have been effective for the basic models, effects such as diffusion and transport require system of reaction diffusion equations. The basic techniques are those of monotone dynamical systems on infinite dimensional spaces. The effect of delays (for example the cell cycle) can also be described in such a context. General techniques for competitive systems on products of ordered Banach spaces, developed in previous work, seem to be applicable. Plasmids are often used in the manufacture of products by genetically altered organisms. Because the plasmid can be lost in reproduction and because the plasmid-free organism is often a better competitor, coding for antibiotic resistance is often included on the plasmid and an antibiotic used in the feed bottle. The differential equation models describing chemostats with inhibitors and plasmids are no longer monotone. The project undertakes the mathematical analysis of such models. The chemostat is a basic piece of laboratory apparatus that models a bio-reactor. The mathematical description of such models takes the form of systems of ordinary differential equations. If the basic assumption of well mixing is removed from the model (there is evidence that it is not satisfied in general) more complicated equations result. The project undertakes the analysis of such model equations using the modern techniques of dynamical systems. The general view is to use the mathematics to point the way to biological (or chemical engineering) experiments with the hope of building better bio-reactors.
