Mathematics

Introduction to Mathematical Biology

Module code: G5106
Level 6
15 credits in autumn semester
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

Mathematical Biology uses mathematical concepts and tools to develop models describing various realistic interactions, such as population size changes, interactions between various biological species, enzyme dynamics and spread of epidemics.

We will introduce a number of mathematical models in Biology. The models are deterministic and the modelling aspect is done via systems of ordinary differential equations.

Topics include famous biology models like the predator-prey model for interacting populations and the susceptible-infected-recovered model for epidemics.

The mathematical techniques used for the analysis of such models are tools from dynamical systems, such as bifurcation analysis.

No previous knowledge of biology is required.

Module learning outcomes

• By the end of the course, a successful student should master techniques for mathematical modelling of population dynamics;
• Non-dimensionalise mathematical models derived;
• Carry out linear stability analysis, phase-plane and graphical analysis of the models;
• Explain some of the concepts of reaction-kinetics such as activation, inhibition, autocatalysis.