Biological Modeling 2023

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Homepage Biological Modeling

The course Biological Modeling is given to Biology undergraduates with a minimal background in mathematics. The aim is that students learn to develop models defined as systems of ordinary differential equations (ODEs), and learn to interpret these models by finding steady states, phase plane analysis and computer simulation.

Learning goals:

  • understand biological processes using mathematical models
  • recognize and master classical mathematical models
  • develop novel mathematical models from scratch
  • simulate mathematical models on a computer
  • be able to linearize models and apply local stability analysis (Jacobi matrix)
  • be able to apply concepts like hysteresis, chaos, periodic behavior, complexity, attractor, and eigenvalue.

Theoretical research plays an important role in modern biology. The course covers a large number of mathematical models to show how one can describe and better 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 development and the analysis of mathematical models. After this course, mathematical models should no longer be considered a "black box". Results obtained by modeling can be critically evaluated based on the assumptions, the complexity, and exact equations of the model. In order to be able to determine the stability of equilibrium we cover a number of mathematical concepts: matrix, eigenvalue, linearization, partial derivatives, Jacobi matrix and complex numbers.

During the course, several mathematical models are developed from scratch. By deducing models from simple biological assumptions, students learn to critically consider alternative models, and gain experience in developing novel mathematical models. Student learn to translate the result obtained by modeling into a biological interpretation.

We work with a number of readers and manuals that are all available on the web: the main reader, its answer book, the math reader, and the Grind tutorial. During the practicals we also work in R and RStudio, using a R-script called grind.R. See the Introduction to R and a tutorial on installing Grind. The models that we use are provide in this folder. Feel free to use these materials for your own education or teaching. I welcome feedback and suggestions for improvement.

For most of the material in the readers and the tutorials simple video clips are provided in the folders BM videos, Math videos, and Tutorials.

Practical information for students attending the course at Utrecht University is provided via the ULearning platform (ULearning), and via Osiris for bachelor and MSc students.