In recent years, much work has gone into applying mathematical methods to biological systems which were often thought to be too complicated to accurately model. One application that has received particular attention from mathematicians is the modeling of cancerous tumour growth in order to better understand and predict the behaviour of cancer. This summer, I began by developing new methods of studying a generalized model which can take the behaviour of three commonly studied models in tumour growth. One such method I worked on was producing new, simplified expressions for certain special cases, which may be calculated directly with much less effort. Once the behaviour of this model was sufficiently understood, I added an additional term to this model to help it better reflect the behaviour of the tumour growth we are studying. This new, more flexible model was examined in a similar manner to the original model to give more convenient methods of manipulating the math behind it.

 I aim to produce a more adaptable version of the model I am studying and give a better understanding of its behaviour.

 If a more quantitative description of cancer may be developed, doctors will be capable of using this knowledge to improve treatment of the disease. For example, if it may be more accurately predicted where tumours will spread, treatment can use a greater focus on key areas to maximize effectiveness while minimizing negative side-effects.

 Before beginning this project, I researched functions known as hypergeometric functions. Unexpectedly, the growth model I was investigating this summer could be expressed in terms of these functions and I was able to apply the results of my previous research to better understand this model. This proved invaluable in the production of simplified expressions. It was gratifying to see that my former research could be used to build on my current research.