Stochastic individual based models
Our main interest in mathematical biology are stochastic, individual based models. These are Markov processes on spaces of point measures, where a point measure describes a populations of individuals (the points) in some space of genotypes, phenotypes (or both) and or geographic space. The transition rates in such a model reflect the key mechanisms that can effect the structure of the population: birth, death, mutations, migration, and interactions between individuals such as competition for resources or other, more direct interactions. Overall, these models are very flexible and can be adapted to many specific situations of interest. We pursue two lines of research in this area:
- Modelling of adaptive dynamics in order to understand generic features of evolution
- Modelling of cancer dynamics and its interplay with therapy in direct collaboration with clinical and experimental physicians. Here is a link to a video that explains the basis of this work for a broader audience (in German).