Investigating a Fractional Derivative Approach to Tumour Growth and Irradiation Modelling

Cancer is one of the foremost causes of death worldwide. Although significant strides forward are continually being made, researchers often revisit foundational questions as newer and better technol- ogy is developed. One fundamental question that piques the interest of clinicians and researchers, alike, is the optimization of cancer- and patient-speci▯c treatment schedules. Mathematical on- cology, while still in its infancy, uses mathematics, modelling, and simulation to study cancer and thus improve our understanding of the disease and its treatments. This thesis focuses on comparing ordinary and fractional di▯erential equation models of tumor growth and radiation. Patient data from the Mo▯tt Cancer Centre is used to ▯t our six candidate models. These results are analyzed to assess the usefulness of the fractional derivative for our particular application and to compare our approach to existing industry standards. Collectively, our analysis shows that mathematical modelling is an invaluable tool to the future of oncology research. iii