# ASO: Mathematical Modelling in Biology - Material for the year 2019-2020

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8 lectures

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.

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.

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.

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

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

G. de Vries, T. Hillen, M. Lewis, J. MÃ¼ller, B. SchÃ¶nfisch. *A Course in Mathematical Biology: Quantitative Modelling with Mathematical and Computational Methods*. SIAM (2006).