| A vast number of mathematical models involve parameters, and hence rely on experimentation and repeat testing to validate a proposed mechanism. Rarely, accurate quantitative results are obtainable. This thesis provides insight into some qualitative conclusions that can be reached irrespective of such parameters for a system of reaction-diffusion equations. The analysis seeks to determine when solution components of reaction-diffusion systems are monotone with respect to a single initial condition. The use of numerous comparison theorems helps answer this basic question. We present a general formulation and continue, in a specific application, to utilize the theory to extend the known monotonicity properties for the SIS epidemic model from that of a system of reaction equations to a system of reaction-diffusion equations. These results are achieved in the absence of explicit solutions to the reaction-diffusion system. |
