Biomedical Mathematics

2019-2020
This course is offered in Dutch. Some of the descriptions may therefore only be available in Dutch.

Course Objective

This course consists of two parts, each with its own goals.

Learning goals part 1:

a. The student is able to write down a statistical model for cellular
evolution;
b. The student can analyse the properties of such models;
c. The student is able to make inferences using these models and perform
generalisations;
d. The student understands the stochastic description of a gene-gene
interaction network and knows how to reconstruct such a network data.

Learning goals part 2:

a. The student is able to model biological processes that involve
time-dependent dynamics (both in discrete and continuous time);
b. The student can perform an analysis of such a model, consisting of
finding steady states and their stability properties using linear
stability analysis, and can describe the effects on solutions of
parameter perturbations;
c. The student is able to interpret the mathematical results back into
the biomedical context;
d. The student is able to study the long-time behaviour of solutions
using the concept of dominant eigenvalues.

Course Content

This course consists of two parts.

The first parts has two sections. In both sections processes in the cell
are modelled. An event in a cell does not occur in isolation, but occurs
in relation to the rest of the cell. In the entire course these
dependencies are modelled. Wherever possible examples from the VUmc
medical hospotical are used to illustrate statistical techniques. In the
first section of this part we focus on modelling DNA sequences. The
resulting models are used to describe the evolution of cancer cells.
Using hidden Markov chain models the exon-intron structure of a gene is
studied. We also describe the evolution of DNA to reconstruct
phylogenetic trees (trees of descent). In the second section, we try to
unravel the topological structure of gene regulatory networks on the
basis of gene expression data. Can we uncover which genes works
together?

In the second part of the course, we will cover deterministic models of
biological processes, both using discrete and continuous time models. We
will treat how to set up equations, analyse the resulting model and how
to interpret the results back into the biological context. We will cover
various biological and biomedical applications, such as ecology,
epidemiology and chemical reactions.

Teaching Methods

Lectures and written assignments

Method of Assessment

For the first part, there is only a written exam. For the second part
there are hand-in assignments (25%) and a written exam (75%). Both parts
need to be passed with a grade of 5.5 or higher.

The resit procedure is as follows. If a student fails to pass one or
both parts, he/she needs to take part in the resit. The resit is one
exam, consisting of two separate parts. If you fail just one part, you
only need to make the questions for that part. For the resit of part 2:
the mark for your assignments only counts only towards your resit mark
if this has a positive outcome on your average mark. If not, the
assignment marks do not count towards the resit mark.

General Information

Course Code X_401056
Credits 6 EC
Period P4+5
Course Level 300
Language of Tuition Dutch
Faculty Faculty of Science
Course Coordinator dr. R. Planque
Examiner dr. R. Planque
Teaching Staff dr. R. Planque
dr. W.N. van Wieringen

Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

This course is also available as: