Introductory description

In this module, we will develop simple models of biological phenomena from basic principles. We will introduce analysis techniques to investigate model dynamics in order to deduce biologically significant results. We will use (systems of) ordinary differential equations, difference equations, and partial differential equations to study population dynamics, biochemical kinetics, epidemiological dynamics, evolution, and spatiotemporal pattern formation. Throughout, we will discuss the biological implications of our results.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

1. Mean-field Population dynamics
   a. Single-species population models
   b. Multi-species population models
2. Models of biochemical kinetics
3. Epidemiological models
4. Models of evolution and game theory models
5. Spatio-temporal models of population dynamics
   a. Travelling waves
   b. Pattern formation

Learning outcomes

By the end of the module, students should be able to:

• To develop models of biological phenomena from basic principles.
• To analyse models of biological phenomena using mathematics to deduce biologically significant results.
• To reproduce models and fundamental results for a range of biological systems.
• To develop an understanding of the biology of the biological systems introduced.

Indicative reading list

H. van den Berg, Mathematical Models of Biological Systems, Oxford Biology, 2011
James D. Murray, Mathematical Biology: I. An Introduction. Springer 2007
Christopher Fall, Eric Marland, John Wagner, John Tyson, Computational Cell Biology, Springer 2002
L. Edelstein Keshet, Mathematical Models in Biology, SIAM Classics in Applied Mathematics 46, 2005.
Keeling, M.J. and Rohani, P. Modeling Infectious Diseases in Humans and Animals, Princeton University Press, 2007.
Anderson, R. and May, R. Infectious Diseases of Humans, Oxford University Press, 1992.
Glendinning, P. Stability, Instability and Chaos, Cambridge Texts in Applied Mathematics, 1994.

Subject specific skills

Students will learn how to derive mathematical models describing biological phenomena from first principles. They will be exposed to different model types (ordinary differential equations, partial differential equations, difference equations) and gain experience in model choice depending on the underlying biological questions. Students will gain analysis skills to determine solution behaviour of model systems and learn how to interpret mathematical results from a biological viewpoint.

Transferable skills

Students will learn about biological systems and the use of mathematical models to solve real world problems. This will be extremely valuable experience for those wishing to use mathematical models in the future in non-academic contexts.