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.
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.
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.