Graeme Wake Centre for Mathematics in Industry, Massey University, Auckland, New Zealand Modelling of cancer treatment Wednesday 30th, June 14:05-15:55pm, Carslaw Building Room 173. Improved treatment of cancer is one of the most important challenges to medical science. Tailoring treatment for individual patients has long been an objective for oncologists. While many biological techniques and mathematical models have been devised to predict the course of treatment, none have been applied routinely to clinical oncology. Our model, which describes the complexities of the responses of tumour cells over time to both anticancer drugs and radiation, has considerable impact on our ability to advance individualisation of cancer therapy. This process is in advanced stages of implementation. Over the last two years, we have developed sophisticated mathematical equations describing the behaviour of cancer cells as they progress through the cell division cycle. Which stage in the cycle the cells are actually in, can be differentiated by their DNA content and this enables model outcomes to be compared directly to experimental results. These equations describe the response of human tumours to chemotherapy and radiotherapy. Firstly we incorporate programmed cell death (apoptosis) into the model. We then consider perturbations of model parameters by treatment, and compare model results with data. This research will provide significant new analytical and computational insights into the area of non-local equations, where cause and effect are separated in "space" and time, as well underpinning support to oncologists concerned with treatment, drug companies producing drugs, and management of clinics.