Introductory description

This course deals with the mathematics behind the dynamics of populations; both populations of free-living organisms (from plants to predators) and those that cause disease. Once the basic models and concepts have been introduced attention will focus on understanding the many complexities that can arise, such as age-structure, spatial structure, temporal forcing and stochasticity. The focus of the course will be how mathematical models can help us both predict the future behaviour of populations and understand their dynamics.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

This course deals with the mathematics behind the dynamics of populations; both populations of free-living organisms (from plants to predators) and those that cause disease. Once the basic models and concepts have been introduced attention will focus on understanding the many complexities that can arise, such as age-structure, spatial structure, temporal forcing and stochasticity. The focus of the course will be how mathematical models can help us both understand the dynamics of populations and predict the future behaviour of these biological systems.

Learning outcomes

By the end of the module, students should be able to:

• At the end of the module, students will be able to: • Describe and analyse classical models in epidemiology and ecology and interpret the biological parameters and model structures. • Understand how to use these models to answer key questions relating to real-world applications; • Perform phase-plane analysis and analyse steady states and their stability to determine how models will behave in various parameter regimes; • Compute the basic reproduction number, R0, using first principles and the next generation matrix approach and use it to assess potential for control of infectious diseases using different intervention strategies. • Implement model analysis for select systems of ODEs, PDEs, and stochastic equations and interpret the results of the analyses; • Critique the modelling assumptions made and suggest ways to improve the models.

Subject specific skills

This module introduces students to applied mathematical epidemiology and ecology. Students will develop the ability to develop their own models of epidemiological and ecological systems, analyse these models and interpret the results in an applied context.

Transferable skills

The ability to model, analyse and interpret results is an important transferable skill that can be used in other applied contexts.