John Alford
Research Interests
My research interests are in modeling, simulation, and mathematical analysis of biological phenomena. I use numerical and analytical techniques from the theory of differential equations (both ordinary and partial) to understand how the model depends on parameters. I am particularly interested in parameters which are heterogeneous (non-constant).
My dissertation work involved computations and analysis of solutions to equations which model the nerve cell called the FitzHugh-Nagumo equations. I was interested in the origins of solutions to these equations which are waves on a circular geometry (rotating waves). Since my doctoral work I have continued to study these equations while both a post-doctoral student at Tulane University and as a faculty member here at Sam Houston State University. They have many fascinating properties and are a good qualitative model of nerve cell behavior.
As a postdoctoral student I became interested in questions from mathematical ecology. I helped to simulate and analyze a reaction-diffusion model (not my own) to eradicate the screwworm fly (an invasive species) by the sterile insect release method. This is an ongoing research project.
Since I have come to Sam Houston State University I have started a new research project on the mathematical modeling of animal movement for a thermoregulating, ectotherm. My work is a collaboration with a biologist here at Sam Houston Dr. William I. Lutterschmidt. We hope to create a mathematical model which may be used to predict how ectotherms move on a heterogeneous thermal microhabitat. This is also an ongoing research project.
Here are some websites that might interest you that are related to mathematical biology:
Society for Mathematical Biology