Effects of combination treatment on a heterogeneous cancer cell population by computational and mathematical modelling

Mathematical models are widely used in cancer drug development to aid understanding the mechanism of action by simulating administration, distribution, metabolism, elimination, and beneficial and adverse effects. In pharmacometrics, ordinary differential equations are commonly used. However, this approach can have limitations when it comes to simulating heterogeneity, spatial distribution, and stochasticity. For example, in oncology understanding the spatial distribution and heterogeneity of the cells is crucial for successful treatment. Therefore, in this thesis different methods such as agent-based models and stochastic models and their combination with ordinary differential equation, and partial differential equations are explored and applied to model heterogeneity of cancer cell populations, the effect of different therapeutic options such as mono and combination therapy and the tumour immune cell interaction. In addition, the reinforcement algorithm is employed to optimise a complex system and to find an optimal treatment given a specific tumour with its parameters and immune micro-environment.