Mathematical modeling in biology, WS 2011/2012

Title: Mathematical modeling in biology

Instructor: Dr. Martin Hutzenthaler, Prof. Dirk Metzler

Time and room:
From October 19, 2011 until February 8, 2012
Lecture: Every Wednesday from 2pm to 4pm
Exercise: Every Wednesday from 4pm to 5pm.
Room: 106, Richard-Wagner Str 10, near Königsplatz

Exam:
February 8, 2012 at 2pm in room 106, Richard-Wagner Str. 10

Contents:
Students will learn how to translate systems from ecology or from population genetics into (implementable) mathematical models. Models for large populations can hardly be implemented efficiently. Therefore our main focus will be on diffusion approximations (both random and deterministic). New results on the implementation of these diffusion models will complement the modeling part.
Structure:

1. Introduction and motivating example
2. One-dimensional stochastic, demographic models
3. Diffusion approximation
4. Multi-dimensional deterministic models
5. Multi-dimensional diffusions
6. Basic test theory
7. Backward processes

Exercise sheets:

• Exercise sheet 01
• Exercise sheet 02
• Exercise sheet 03
• Exercise sheet 04
• Exercise sheet 05
• Exercise sheet 06
• Exercise sheet 07
• Exercise sheet 08
• Exercise sheet 09
• Exercise sheet 10
• Exercise sheet 11
• Exercise sheet 12

Simulating ordinary differential equations:

• A simple graphical tool is Populus. This little tool has been programmed for teaching porpuses.
• A powerful tool for numerics is MATLAB. Here is a short Matlab-file to have some examples: odes.m (you also need firstode.m and Lotka.m to run it).
• Unfortunately, MATLAB is not for free. Instead you might want to use Octave which is similar to MATLAB.
• If you know the statistics language R already, then you can do simulations also in R. Here is a little example file: Lotka.R. For downloading and using R, see An introduction to R.

Requirements: Basic knowledge of a lecture on probability theory or on stochastic processes.

Language: English (German if preferred by all attendees)

Questions: Please send any question to hutzenthaler@biologie.uni-muenchen.de

A short email is welcome to estimate the number of attendees.