Mathematical modelling of cancer growth and treatment

Abstract

Over the last few decades, tumour cell dynamics has become very well-researched by means of clinical, experimental, and theoretical approaches. This has brought about both a better understanding of tumour growth and a more comprehensible perspective on treatment strategy. Models comprising of both ordinary differential equations as well as partial differential equations will be considered. There is strong evidence in literature, that the cellular immune system of the human host has a direct influence on tumour growth. The natural killer cells and CD8+ T cells are two major components of the immune system which are known to have a demanding role in the eliminating of tumour cells. Moreover, the dendritic cells (antigen-presenting cells) are another constituent which play a fundamental role in stimulating and activating the immune system. In addition to this, over recent years they have also been reported to directly destroy tumour cells. A mathematical model will be developed to investigate the theoretical description of this biological system. This will be thoroughly analysed in order to extract quantitative as well as qualitative findings. Furthermore, systems which depict thyroid function and malfunction will be looked into in which the main biochemical reactions involved: iodine entry, its binding to thyroglobulin, and thyroxine formation, are highlighted. The main aim of this project is to accentuate the importance of mathematical modelling in the field of cancer research. This analysis will be facilitated with the use of Wolfram Mathematica which will aid in the mathematical solving of equations as well as in the plotting of their graphical representations.