Exploring Modeling by Programming: Insights from Numerical Experimentation

This chapter aims to provide students the background necessary to use computational methods and numerical experimentation to pursue mathematical research. We provide a brief refresher on differential equations, model building, and programming, followed by in-depth discussions of how numerical experimentation was critical to three undergraduate research projects involving parasite transmission in feral cats, the role of protein regulation in establishing circadian rhythms, and treatment costs in an influenza outbreak. Code (written in R) is provided for most of the models and nearly all of the figures presented in the chapter, so that the reader may learn the programming as they go along. We also propose ideas for extending the research projects presented in the text. Both deterministic and stochastic models are presented and the critical role of computational methods in obtaining solutions is illustrated.