My research focuses on analysis and numerical simulations of nonlinear partial differential equations (PDE) which
arise from biology. Models I am working on are for example
Population dynamics and resistance to therapies
Chemotaxis in a fluid
Aerosols in the lung
Research > Population dynamics and resistance to therapies
We are interested in the Darwinian evolution of a population structured by a phenotypical trait which directly influences growth.
This phenotypic trait can be e.g. the length of the
giraffe's neck or the shape of beaks of
Two principles, proposed by Darwin, form the basis for evolution in these models:
- Mutation: The traits of individuals can change slightly when they are passed on to their descendants,
- Selection: Individuals whose traits are better adapted to the environment in which they live reproduce with a higher probability.
These models from population dynamics can help to understand why resistances against drugs develop in therapeutic processes.
E.g. resistance to chemotherapy
occurs when cancers that have been responding to a therapy suddenly begin to grow. In general, resistance is a
quite common feature in diseases like malaria as well as infections caused by bacteria or viruses.
Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance phenotype in Lorz et al. This phenotype influences birth/death rates, effects of chemotherapies (both cytotoxic and cytostatic) and mutations in healthy and tumor cells. We extend previous work by demonstrating how qualitatively different actions of cytostatic (slowing down cell division) and cytostatic (actively kills cells) treatments may induce different levels of resistance.
We also derive the long-term temporal dynamics of the fittest traits in the regime of small mutations.
The picture below shows one of the results from this paper: in our models the combination of cytostatic and cytostatic treatments are much more effective against cancer cells while keeping alive more healthy cells