Speaker：Prof. Jim Grannell（School of Mathematical Sciences, UCC）
Topic：Mathematical Modelling in Pharmacology
Place：Room 422, School of Mathematics and Statistics
Abstract : This subject is quite new and has been developed mainly by pharmacologists. The initial successful approaches were purely statistical. These models provided clues to the underlying processes which involve a knowledge of anatomy, physiology, and biochemistry and these insights have enabled the development of process‐based models. I start with a review of history and concepts arising in pharmacology models. I then consider a few simple models to illustrate a range of mathematical problems that arise in this area - systems of nonlinear ordinary differential equations and systems of nonlinear algebraic equations. The differential equations are singularly perturbed and involve a number of small parameters. I have developed an asymptotic matching approach to the solution of such systems. I review a few models developed jointly with clinical colleagues at Cork, Sheffield and Manchester universities and the company SIMCYP, UK - pain management for liver cancer surgery and a number of drug‐drug interactions.