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Cursus: B-MBIMOD
B-MBIMOD
Biological Modeling
Cursus informatie
CursuscodeB-MBIMOD
Studiepunten (EC)5
Cursusdoelen
  • understanding biological processes by mathematical modeling
  • know and understand classical mathematical models
  • develop novel mathematical models from scratch
  • simulate mathematical models on a computer
  • know how to apply local stability analysis (Jacobi matrix)
  • know how to apply the concepts hysteresis, periodic behavior, complex systems, chaos, attractor, eigenvalue.
Inhoud

Theoretical research plays an important role in biology. The course covers a large number of mathematical models to show how one can describe and understand the dynamics of biological populations. Examples of this population dynamics are: ecological food chains, epidemiological models, bacteria infected by phages and populations of cells. Students are made familiar with the preparation and analysis of mathematical models. After this course, mathematical models should no longer be considered a "black box". Results of models, and their biological consequences, must be critically weighed based on the content, complexity, reality, and formalism of the model.

During the course classical mathematical models are developed from scratch. By deducing models ourselves from simple biological assumptions, the student learns to critically consider such models and gains experience in developing mathematical models themselves. The student learns to translate the results obtained with such models into a biological interpretation. In order to be able to determine the stability of equilibrium we treat a number of new mathematical concepts such as: matrix, eigenvalue, partial derivatives, Jacobi matrix and complex numbers. 

The course runs for the first 7 weeks of period 1.  The first week refreshes the required mathematical background (basic algebra, sketching functions), covers the basics of linear algebra (matrixes, eigenvalues, Jacobi matrix), and can be done as self study because we provide online tutorials. During week 2 – 6 we cover the material in the eBook Biological Modeling by having 15x2h lectures (in the morning) and paper/pen and computer practicals in the afternoons of timeslot BC. At the end of week 7 there is a written exam.

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