Mathematical Biology module (MA41008)

Mathematical Biology shows how mathematics can help explain living systems. In this module, you will learn how differential equations can be used to model biological processes that change over time, spread through space, or form patterns.

You will begin with models from enzyme kinetics and population dynamics. These examples show how mathematical equations can describe growth, interaction, feedback, and change in biological systems.

You will then study partial differential equation models in biology, including diffusion and reaction-diffusion equations. These models help explain how biological quantities move and interact across space and time. You will explore Fisher’s equation and travelling wave solutions, which can describe processes that spread through a population or tissue.

A central theme is biological pattern formation. Through Turing’s pre-pattern theory, you will see how simple mathematical rules can generate spatial patterns, with applications to animal coat markings and how biological shapes form during development.

You will also study epidemiological models and models of nerve signal propagation, showing how mathematics can be used to investigate disease spread and electrical activity in biological tissue.

By combining modelling, stability analysis, travelling waves, and biological interpretation, this module develops your ability to use mathematics to understand complex behaviour in living systems.

What you will learn

In this module, you will:

• model biological systems using nonlinear differential equations
• study enzyme kinetics and population dynamics
• explore diffusion and reaction-diffusion equations
• analyse Fisher’s equation and travelling wave solutions
• investigate Turing pattern formation, including animal coat patterns and biological shape development
• study epidemiological models and nerve signal propagation
• interpret mathematical results in a biological context.

By the end of this module, you will be able to:

• formulate mathematical models for biological processes
• analyse steady states and assess their stability
• use differential equations to study spatial and temporal behaviour
• predict when spatial patterning may arise
• analyse travelling wave solutions
• connect mathematical model behaviour to biological interpretation

Assignments / assessments

• Coursework (20%)
• Written exam (80%)

Teaching methods / timetable

• lectures, introducing analytical and numerical methods for ordinary and partial differential equations
• worked examples, showing how approximation methods are constructed, analysed, and applied to model problems
• tutorials, where you will practise solving problems involving stability, convergence, error analysis, and finite difference methods