ASO: Mathematical Modelling in Biology - Material for the year 2020-2021

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2020-2021
Lecturer(s): 
Prof. Philip Maini
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 how to model various processes in ecology, epidemiology, chemistry, biology and medicine, using ordinary differential equation models, as well as an introduction to discrete models. It demonstrates how mathematical techniques such as linear stability analysis, phase planes, perturbation and asymptotic analysis 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 continuous-time non-spatial models.

Course Synopsis: 

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

Discrete time models for single species – linear stability analysis and cobwebbing.

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

Enzyme-substrate kinetics, the quasi-steady state approximation and perturbation analysis.

Modelling of neuronal signalling using the Hodgkin-Huxley model and excitable kinetics.

Infectious disease modelling including SIR models.

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).