Mathematical Modelling is the approach to describe a complex natural phenomenon with mathematical concepts such as differential equations or stochastic processes. The advantage of this approach is that mathematics provides a useful toolbox to address a given complexity and make biological inferences that were not possible based on sole intuitive reasoning. On the other hand, mathematics can benefit from modelling as well. Often, a biological question leads to a new type mathematical model (eg. a certain system of ODEs) and a mathematical problem within that model (eg. long-term behavior or existence of non-trivial equilibria).
In this talk, I will discuss the interplay between mathematics and biology/medicine on the basis of selected examples, such as neural stem cells, tumor growth and pattern formation in living organisms.