ASO: Mathematical Modelling in Biology (2016-2017)

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2016-2017
Lecturer(s): 
Prof. Ruth Baker
Course Term: 
Trinity
Course Lecture Information: 

8 lectures

Course Overview: 

Mathematical Modelling in Biology introduces the applied mathematician to practical applications in an area that is growing very rapidly. The course focuses on examples from population biology that can be analysed using deterministic discrete- and continuous-time non-spatial models, and demonstrates how mathematical techniques such as linear stability analysis and phase planes can enable us to predict the behaviour of living systems.

Learning Outcomes: 

Students will have developed a sound knowledge and appreciation of the ideas and concepts related to modelling biological and ecological systems using both discrete- and continuous-time non-spatial models.

Course Synopsis: 

Discrete population models for a single species including oscillations, bifurcations and chaos.

Discrete models for interacting populations.

Continuous population models for a single species including hysteresis, harvesting and delays.

Modelling interacting populations, including predator-prey and the principle of competitive exclusion.

Infectious disease modelling.

Reading List: 

J. D. Murray, Mathematical Biology, Volume I: An Introduction. 3rd Edition, Springer (2002).

Further Reading: 

N. F. Britton, Essential Mathematical Biology. Springer (2003).

G. de Vries, T. Hillen, M. Lewis, J. Müller, B. Schönfisch. A Course in Mathematical Biology: Quantitative Modelling with Mathematical and Computational Methods. SIAM (2006).