Mathematical modelling - population growth models in the context of biological tumor
In this talk, we first introduce the basic principles of mathematical modelling. We then understand the basic SIR model for spread of diseases. The talk introduces population growth models based on the ODE approach and relates these to tumor growth. Consequently, the PDE approach will be introduced for a single species and multiple species within a tumor environment. These are coupled PDEs which can be treated via mathematical analysis, analytical techniques or numerical simulations. Some test cases will be shown. Finally, a biphasic mixture model to capture the hydro mechanical behaviour of a biological tumor will be introduced as a coupled parabolic-hyperbolic type PDEs. Existence and uniqueness results will be briefed.