Bakerian Prize Lecture
Professor James Murray FRS University of Oxford
Practical mathematical models are becoming an accepted part of most medical and scientific disciplines. They cover an ever expanding spectrum of topics. A few of the more unlikely applications are justifying intertribal warfare, the benefits of cannibalism, how the leopard gets its spots, how sex determination in crocodiles has let them survive and demonstrating the connection between badgers and bovine tuberculosis. This lecture shall describe the modelling of two applications.
The prognosis for patients with high grade brain tumours is grim and the various treatment protocols such as surgery, radiation and chemotherapy cannot effect a cure. A simple model using patient data and brain scans quantifies the spatio-temporal growth of brain tumours. Analysis of the model shows how difficult it is to decide on the tumour volume to be treated and shows why such treatments have so little success. The model simulations can estimate life expectancy for the patient and show how it might be possible to use a patient's past record to quantify possible treatment efficacy.
The rise in divorce rates in developed countries is a widespread but poorly understood phenomenon. A simple but surprisingly predictive mathematical model, based on only a few parameters describing specific marital interaction patterns, has helped design new scientifically-based intervention strategies for troubled marriages which are proving encouragingly successful in clinical practice. In a 12-year longitudinal study on a large number of marriages, the model has predicted divorce with an accuracy of 94%.