Introductory description

In this module, we will develop simple models of biological phenomena from basic principles. These models will then be analysed to investigate their stability in order to deduce biologically significant results. We will use applications from population dynamics, systems biology and epidemiology and derive differential equations to explore how biological systems evolve and the impact of model structure upon model stability. Finally, 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. General introduction to mathematical biology, its uses and successes.
2. Population Dynamics and Epidemiology 2.1Simplemodelsofbiologicalpopulations 2.2Simplemodelsofinfectiondynamics 2.3Introducingmorecomplexity–risk structures 2.4Realworldexample:ZikavirusinBrazil. 3. Systems Biology 3.1Modellingregulatoryandsignallingsystems 3.2Modellingthecellcycles 3.3Realworldexample:optimaltreatmentofcancersusingchemotherapy.

Learning outcomes

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

• To develop simple models of biological phenomena from basic principles.
• To analyse simple models of biological phenomena using mathematics to deduce biologically significant results.
• To reproduce models and fundamental results for a range of biological systems.
• To have a basic 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

This is a 15 lecture taught model. Students will also complete three assignments that will be supported by a weekly examples class. The course will be assessed with a 1 hour exam.

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.