Term(s): Term 2
Status for Mathematics students: List C
Commitment: 30 one-hour lectures
Assessment: 100% 3-hour examination
Formal registration prerequisites: None
Assumed knowledge: No formal prerequisites. Some practical knowledge of how to analyse and solve differential equations will be assumed. In particular, finding fixed points and their stability in systems of ODEs, drawing phase plane diagrams, solving difference equations, a very small amount of PDEs etc.
Synergies: This course complements MA4M1 Epidemiology by Example, and the two courses are designed to work separately, concurrently, or one after the other.
Content: This course deals with the mathematics behind the dynamics of populations; both populations of free-living organisms (from plants to predators) and those that cause disease. Once the basic models and concepts have been introduced attention will focus on understanding the many complexities that can arise, such as age-structure, spatial structure, temporal forcing and stochasticity. The focus of the course will be how mathematical models can help us both predict the future behaviour of populations and understand their dynamics.
Research into the dynamics of ecological populations allows us to understand the conservation of endangered species, make predictions about the effects of global climate change and understand the population fluctuations observed in the natural world. Work on infectious diseases clearly has important applications to public-health, allowing us to predict the spread of an epidemic (such as Foot-and-Mouth or SARS virus) and determine the effect of control measures.
Throughout, use will be made of examples in the recent literature, with a strong bias towards read-world problems. Special attention will be given to the applied use of the models developed and the necessity of good quality biological data and understanding.
Much of this course will be based on research papers and comprehensive references will be given throughout the course. Four useful books are:
R.M. Anderson and R.M. May, Infectious Diseases of Humans, Oxford University Press, 1992. (ISBN 019854040X)
S.P. Ellner and J. Guckenheimer, Dynamic Models in Biology, Princeton University Press, 2006 (ISBN 0691125899)
R.M. May and A. McLean, Theoretical Ecology: Principles and Applications, Oxford University Press, 2007 (ISBN 0199209995)
M.J. Keeling and P. Rohani, Modelling Infectious Diseases in Humans and Animals, Princeton University Press, 2007 (ISBN 0691116172)