PhD student Hasitha is supervised by Dr Pamela Burrage and Dr Dan Nicolau. She is working on agent-based and differential-equation models of tumour growth and is due to complete her thesis within the next few months. The description of her project is included below: Mathematical Modelling for the Tumour Microenvironment (TME) under Cellular Stress By studying the complexity of the tumour microenvironment (TME), we can identify how tumour cells become invasive under different circumstances. In this study, tumour cell behaviour under cellular stress of the TME is observed using discrete and continuum mathematical modelling techniques. An agent-based model is developed to study individual cell behaviour of the TME. Under this agent-based model, we observe how interactions between tumour cells, normal cells, and the extra cellular matrix (ECM) promote tumour progression and invasion. This agent-based model is extended to discover possible treatment options after diagnosing the disease. To study the tissue level dynamics, continuum models for the TME are developed. Firstly, we develop a system of ordinary differential equations (ODEs) using the equation-learning (EQL) method with simulation results of the agent-based model. Additionally, we develop a system of ODEs by considering interactions between normal cells and tumour cells. Furthermore, we develop two systems of stochastic differential equations (SDEs) by considering alternative formulations of the Chemical Langevin Equation (CLE). Different mathematical models developed in this study suggest that understanding cell communication in the TME supports identification of important tumour microenvironmental factors that may cause tumour cell malignancy.