Analysis Seminar

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Population Dynamics and Therapeutic Resistance: Mathematical Models

Speaker: Alexander Lorz, University Paris 6

Location: Warren Weaver Hall 1302

Date: Thursday, May 26, 2016, 11 a.m.

Synopsis:

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.