Analysis of a Reaction-Diffusion Model Towards Description and Prediction of Breast Cancer Progression

Abstract

This thesis conducts a thorough investigation by combining mathematical analysis, empirical clinical data, and meticulous clinical observations to investigate the tumour dynamics which are controlled by two crucial biomarkers: cancerous cells (CK7) and active T-cells (CD4). Introducing a reaction-diffusion model facilitates the spatial and temporal distribution of the biomarkers CK7 and CD4. Subsequently, explore the stability, bifurcation and sensitivity analyses to show the effects of critical biological parameters on tumour dynamics. An exploration of the travelling wave solutions of the model, through numerical methods, aids in the visualisation of the dynamic behaviour of the system, particularly the invasion of the CK7 population towards the CD4 population. Employing a numerical approach, specifically utilising the finite volume method, provides a clear representation of the dynamic interplay within the tumour environment. Our analysis contributes not only to a heightened theoretical understanding but also holds potential implications for therapeutic decisions in tumour dynamics. Hence, our investigation shows efficacy not only in predicting tumour dynamics but also in providing a robust framework to present specific clinical observations.