Mathematical Models in Biology

Introduction in theory and application of dynamical systems and stochastic processes: linear compartmental models, Markov-chains, Galton-Watson processes, birth-death-processes, population models, spatial models and age structured models.

This module imparts the ability to formulate mathematical models for biological systems on the basis of analytic, stochastic or discrete mathematical structures. The emphasis of the module is to teach the understanding of the importance for different model approaches for one single biological system. At the end of the module, the student is able to evaluate the connection of different results related to different model approaches (stochastic/deterministic, discrete/continuous) and to choose the appropriate level for the description of the system under observation.

MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Linear Algebra and Discrete Structures 2, MA1401 Introduction to Probability Theory
Bachelor 2019: MA0001 Analysis 1, MA0002 Analysis 2, MA0004 Linear Algebra 1, MA0005 Linear Algebra 2 and Discrete Structures, MA0009 Introduction to Probability Theory and Statistics

lecture, exercise course, self study exercises

blackboard

J.D. Murray, Mathematical Biology. Springer-Verlag, 3rd ed. in 2 vols.:
Mathematical Biology: I. An Introduction, 2002;
Mathematical Biology: II. Spatial Models and Biomedical Applications, 2003;
P. Jagers: Branching Processes With Biological Applications. Wiley, London 1975

The module examination is based on a written exam (60-90 minutes) or an oral exam (20-30 minutes). Students have to understand basic analytic, stochastic and discrete structures to model biological systems and can evaluate the connection of different results related to different model approaches. They are able to choose the appropriate models.