Generally I am interested in the genuine application of mathematical modelling in biology, medicine and psychology. Pedagogically I am also interested in communicating the excitement and practical use of scientific research, primarily 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. All of the research is interdisciplinary and usually collaborative with experimental biomedical scientists.

I am currently interested in the growth and control of brain tumours, specifically gliomablastomas, the most common and aggressive brain tumour and which is always fatal. Our models can estimates life expectancy, quantify specific treatments, namely surgery, radiation  and chemotherapy, for individual patients prior to their use and fairly accurate. Other areas of current research are: (i) modelling marital interaction and divorce prediction and the development of a scientifically based marital therapy; (ii) benefits of cannibalism; (iii) specific species extinction which could result from climate change, specifically mild temperature rise.

Some examples of my 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 with relevance to human craniofacial development, 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 the true level of blood alcohol; wound healing and scar formation; medication levels for hyperlactatemia in diabetics; morphogenetic laws.  The 3^rd edition of my book (in 2 volumes), Mathematical Biology, 2003, 2004, describes many examples in detail.