Entry requirements

150 credits complete courses including Biology 75 credits, chemistry 30 credits and Mathematics and statistics 10 credits.

Learning outcomes

The major aim of the course is to give students with biological background an understanding of, and experience in, using mathematical models of biological systems. After passing this course the student should be able to:

• account for the principles behind modelling - why one uses mathematical models
• account for how to design and use a model - mathematical formulation of problem, development of equations, the model cycle and interpretation of results
• account for properties of some basic models - discrete and continuous time models, differential equations, logistic growth and models for species interactions, models of genetics, stochastic models and models within epidemiology, spatial models and class structured models
• analyse equations - analysis of equilibrium and stability, basic numerical methods
• critically interpret scientific papers that are based on models

Content

• How to design a model: To formulate a question; quantitative versus qualitative models, the model cycle.
• Classical models in biology: Population growth models; models of natural selection; models of interactions between species.
• Stability analysis: Equilibrium and stability in one-dimensional models; linear and non-linear models; repetition of linear algebra; equilibrium and stability in two-dimensional models; analysis of phase diagrams.
• Stochastic models in biology: Basic probability theory, the models of Wright-Fishers and Morans for allelic frequencies.
• Class structured populations: Matrix algebra and Leslie matrices. Spatial models: Drift and diffusion equations, Fishers equation for gene dispersal.

Instruction

Lectures, problem-solving and computer exercises.

Assessment

Written assignments that combine analysis and numerical solutions (25% of the total of points of the examination). Examination at the end of the course (75%).