Mathematical Modeling

Biomathematical Modeling is a very strong and active research focus of the Department of Computational Medicine.  Biomathematical Modeling provides the framework and general theory consistent for expanding and exploring biological concepts and questions. In this way, it’s a driving force behind how we understand all of life, health, and medicine. Examples in this endeavor include quantifying viral infection under different physiologic conditions, understanding stem cell repopulation after transplantation, providing insight into growth and treatment of cancer devising strategies for slowing evolution of drug resistance, quantifying the effects of different molecular factors in cell signaling pathways, quantifying vascular pathologies and effects on tissue growth and death, understanding pattern formation and swarming, and predicting amounts and function of sleep. 

Models of these phenomena typically emphasize the biological system with a few key principles, assumptions, and parameters as possible. Experimental and empirical data are used to ground these models by testing which assumptions, behavior, and predictions match the real world. This approach allows a deeper understanding of which factors dominate the dynamics and structure of the system, helps prevent over-fitting and over-interpretation of data and makes tractable comparisons to empirical data, design of new experiments, analytical calculation, and computer simulations.

The mathematical and statistical methods used to generate these models, determine their properties, validate them, estimate parameters, and make predictions are highly variable and include: optimization and numerical methods, reaction kinetic theory, stochastic simulation, statistical mechanics, maximum likelihood estimation, probability theory, Markov chain and branching processes, and time-series analyses.  Research in the Department includes not only the application and improvement of these existing methods but also the development of novel methods.