- Program in Applied and Computational Mathematics
I am interested in mathematical modelling in biology, medicine and psychology. Pedagogically I am also interested in communicating the excitement and practical use of scientific research, primarily practical mathematical modelling, to the general public. I try to construct realistic models to reflect the known biology, then study the resulting mathematical models and compare the results with extant experimental data. The final aim, and frequent result, is to be able to make biomedical predictions which can be confirmed by experiment or further observation.
I am currently interested in the growth and control of brain tumours, specifically gliomablastomas. The models can estimates life expectancy, quantify specific treatments, namely surgery, radiation and chemotherapy, for individual patients prior to their use. Other areas of current research are: modelling marital interaction and divorce prediction; benefits of cannibalism; specific species extinction which could result from climate change, specifically mild temperature rise. A few examples of past research are: animal coat patterns (How the Leopard Gets its Spots); butterfly wing patterns; the growth and detection of prostrate cancer; mechanisms for the spatial patterning of teeth initiation in alligators, spatial spread of rabies epidemics; bovine tuberculosis as related to a badger-cattle interactions; social behavior in certain animal communities and its importance in territory formation and survival, breathalysers and their accuracy in predicting blood alcohol level; wound healing and scar formation; predictive morphogenetic laws.