My research is centered around dynamical systems models of biological or other processes. It is weighted toward the applied end of the mathematics spectrum, often concerned with implementation details and issues of making the mathematics accessible to biologists and engineers. My research spans a wide set of disciplines, including algorithm development, numerical analysis, dynamical systems, mathematical modeling, and bifurcation theory, but dynamics is a unifying theme throughout.
I enjoy working closely with experimentalists helping solve the problems in which they are interested, but am also interested in the more mathematical issues which often surface from this research.
Many of my master's students have gone on to Ph.D. studies, and one has completed teacher's college and is currently working as an I.T. training specialist. Two of my Ph.D. students have gone on to post-doctoral work, and one now has a faculty position.
- Climate change modelling
- Mathematical biology
- Bifurcation with symmetry
- Parameter estimation
- Neuronal ion channel modelling
- Dynamical systems.
- An Energy Balance Model of Climate Change Incorporating the Roles of Carbon Dioxide and Water Vapour as Greenhouse Gases
Brady Dortmans, Master of Science (2017).
- Mathematical Analysis of a Delay System as an Equivalent Model for a Size-Structured Fish Population
Mona Ghwila, Master of Science (2017).
- Models of Cytokine Dynamics During Cytokine Storms and Synergy During Virus and Drug Combination Therapy
Marianne Waito, Doctor of Philosophy (2016).
- Parameter Range Reduction in Systems of Differential Equations
Andrew Skelton, Doctor of Philosophy (2014).
- A Model of the Effects of Fluid Variation Due to Body Position on Cheyne-Stokes Respiration
Marianne Wilcox, Master of Science (2013).
B.Math. (University of Waterloo).
M.Math. (University of Waterloo).
Ph.D. (Cornell University).
- Brady Dortmans, William F. Langford, Allan R. Willms, 2019. An energy balance model for paleoclimate transitions, Climate of the Past 15 (2), pp. 493-520, doi=10.5194/cp-15-493-2019.
- Allan R. Willms, Petko M. Kitanov, 2018. Probability of Escherichia coli Contamination Spread in Ground Beef Production, Mathematical Biosciences & Engineering 15 (4), pp. 1011-1032, doi=10.3934/mbe.2018045.
- Allan R. Willms, Petko M. Kitanov, William F. Langford, 2017. Huygens' Clocks Revisted, R. Soc. Open Sci. 4 (170777), doi=10.1098/rsos.170777.
- Marianne Wilcox, Allan R. Willms, William F. Langford, 2015. A Model of the Effects of Fluid Variation due to Body Position on Cheyne-Stokes Respiration, Bulletin of Mathematical Biology 77 (3), pp. 488-498,doi=10.1007/s11538-015-0064-x.
- Andrew Skelton, Allan R. Willms, 2015. Parameter Range Reduction in Ordinary Differential Equation Models, Journal of Scientific Computing 62 (2), pp. 517-531, doi=10.1007/s10915-014-9865-6.