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Advanced Topics in Applied Probability (V5F5)

Stochastic Models in Life Science

Time and place: Monday and Wednesday, 10 (c.t.) -12, Zoom

The lecture is now available on eCampus. Please register there for the course to gain access to the Zoom link and all other materials connected to the lecture. The handwritten lecture notes and video recordings of the live lectures will be accessible through a Sciebo folder (link available on eCampus).

If you want to follow the course but do not have an eCampus account, please write an email to kraut (at) iam.uni-bonn.de to get the links to the meeting and the Sciebo folder.

Office hour: From now on there is an open question session every Friday, 9:30-10:30 am, under the same Zoom link as the lecture. 

Complementary talk series: The lecture is accompanied by a series of talks (Ringvorlesung) that provides insight into biomedical questions that can be tackled with the help of mathematics. Each week there will be a guest lecture either on Monday or Wednesday before the main lecture (9 s.t.). The schedule and the Zoom details can be viewed here.
The first talk will be on Wednesday 28th April, 9:00 am!

Content of the lecture: The lecture will evolve around so-called "individual-based models of adaptive dynamics". These are measure-valued continuous-time Markov processes that describe the evolution of heterogeneous populations, subject to the mechanisms of birth, death, competition, and mutation. In the lecture we will focus both on the theoretic study of such models, giving insights into the long-term adaptive evolution of a population, as well as their applications in modelling of complex biological systems, allowing to answer questions that arise in medical research.

The main topics that will be covered are:

  • Construction and properties of individual-based models of adaptive dynamics
  • Scaling limits under different regimes of large populations, rare mutations, and small mutation step sizes
  • Variations of the classical model that consider diploid systems or phenotypic switches
  • Applications to the study of cancer immunotherapy and possibly other biomedical questions

Lecture notes from when this course was given two years ago can be found here. They will be updated over the course of the semester. The final version will be linked on the website. An intermediate version is accessible via eCampus.

Exam: oral via Zoom, end of July