Thu, 23.06.2016, 16:00

Thu, 23.06.2016, 17:00
Population dynamics and therapeutic resistance: Mathematical models
Kolloquium Angewandte Mathematik

Referent: Dr. Alexander Lorz (Université Pierre et Marie Curie - Paris, LJLL)
Veranstalter: Eberhard Bänsch
Raum: Seminarraum 04.363

Abstract: We are interested in the Darwinian evolution of a population structured by a phenotypic trait. In the model, the trait can change by mutations and individuals compete for a common resource e.g. food. Mathematically, this can be described by non-local Lotka-Volterra equations. They have the property that solutions concentrate as Dirac masses in the limit of small diffusion. We review results on long-term behaviour and small mutation limits. A promising application of these models is that they can help to quantitatively understand how resistances against treatment develop. The population of cells is structured by how resistant they are against a therapy. We describe the model, give first results and discuss optimal control problems arising in this context.