The project looks at the proliferation and motility of biological populations. These populations evolve in a competitive and changing environment. They grow, shrink and move according to laws of reproduction and interaction under the effect of random events.
Such populations arise when a mutant gene appears in an established population or when a cancer cell appears in a healthy tissue or becomes irradiated. Most of mathematical biology assumes deterministic and differentiable models. However, the appropriate treatment of such finite but large systems must be done by stochastic analysis to discover finer effects of random fluctuations. The theoretical results uncovered by this project will find applications in evolution and cancer modelling.