Mathematical Biology
Mathematical Biology for Life Scientists
Biologie mathématique et biosimulation
Quantities observed in biology change as a function of time:
the population of a given species may grow or decay;
the immune system reacts to a viral infection;
cells are excited and generate electrical pulses;
organisms take form and shape during development.
This course focuses on nonlinear differential equations
to describe these and other biological
phenomena (population growth, predator-prey models,
immune system, biophysics of membrane excitability).
Lectures ex cathedra are complemented by Computer Exercises
using MatLab and paper-and-pencil exercises.
Contents
- Population Models for Single Species
- Continuous Models of growth and death
- Population Models for Interacting Species
- predator-prey models, Lotka-Volterra
- Reaction Kinetics
- enzyme kinetics, gene regulation, Michaelis-Menten
- Biological Oscillators
- feedback control
- qualitative analysis of 2-dim. systems
- Membrane Excitability
- Hodgkin-Huxely model
- FitzHugh Nagumo model
- Viral Infection and Immune control
- Immune response models
- Formation of Spatial Patterns
- Stripe formation
Textbook: J.D. Murray, Mathematical Biology (Springer)
Exercises
-
Weekly exercises
- Miniproject. The miniproject will count 1/4 towards the final grade.
The miniproject will be given in week 10 and needs to be handed
in on June 10 at 11h00.
Exam
There is a written exam in the final week.
The results of the written exams count 3/4
and the miniproject 1/4 towards the final grade.
Written Exam on June 14 at 8h15-11h00 in
rooms EL A1 (names starting with A-R) and ELD120
(names starting with S-Z) .
The written exam covers all topics of the course.
The style of the exam will be similar to
that of the midterm exam in week 8.
Oral Examination of Miniproject on June 7 at 14h00-16h00
- presence is mandatory. Everybody
needs to be in the computer room C020-23 for
a control of their matlab program of the miniproject.
The deadline for the written report
of the miniproject is June 10 at 11h00 .
The miniproject has a maximum of 3 pages.
Even if you hand in more than 3 pages, we will
only read the first 3 pages and
disregard the rest.
There is a midterm exam in week 8.
If the result of midterm exam is better
than that of the final exam, it counts
1/4 towards the final grade (and the final exam 2/4).
Otherwise the final exam counts 3/4 and
the midterm is not taken into account.