Module code: MAT3040

Module provider


Module Leader

GOURLEY SA Prof (Maths)

Number of Credits


ECT Credits



FHEQ Level 6

JACs code


Module cap (Maximum number of students)


Module Availability

Semester 2

Overall student workload

Lecture Hours: 33

Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test IN-SEMESTER TEST 20%
Examination EXAMINATION 80%

Alternative Assessment


Prerequisites / Co-requisites

MAT2007 Ordinary Differential Equations

Module overview

An introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.

Module aims

introduce students to basic principles involved in mathematical modelling in ecology and epidemiology

give students an appreciation of how ordinary differential equations, delay differential equations and partial differential equations can apply in various ecological and epidemiological scenarios

teach appropriate analytical techniques for studying such models

give students an appreciation of how to interpret the results and make predictions

Learning outcomes

Attributes Developed
An understanding of how to model ecological and epidemiological problems using differential equations (ordinary, partial and delay) KCT
An understanding of appropriate analytical techniques for the study of such problems KC
An understanding of how to interpret the results of the analysis and how to make predictions KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

Indicative content includes:

Review of simple ODE models in ecology such as the logistic and Lotka-Volterra models. Extensions of such models such as the use of the Holling functional responses. Phase plane analysis of such models.
ODE models in epidemiology. The Kermack McKendrick model. Higher dimensional models that include, for example, an exposed compartment, or which incorporate treatment, vaccination or quarantining. Analytical techniques useful in the linearised analysis of high dimensional systems, such as the Routh Hurwitz conditions. The calculation of the basic reproduction number and its importance in epidemiological modelling.
Age structured models and their reformulation into delay differential equations or renewal integral equations. The study of the characteristic equations resulting from the linear stability analysis of such models. Use of such equations in ecology and epidemiology, to include the Ross Macdonald model of malaria transmission. The basic reproduction number for models with delay.
Reaction-diffusion equations. Travelling wave solutions; applications to ecology and epidemiology.  

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

Skills in modelling ecological and epidemiological phenomena mathematically
Knowledge of mathematical techniques appropriate to the study of those problems.
An appreciation of how to interpret the results and make ecological or epidemiological predictions as appropriate.

The learning and teaching methods include:

3 one-hour lectures per week for 11 weeks, involving traditional lecturing and class discussion.


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

·         Understanding of how to model real life ecological and epidemiological scenarios, and an understanding of the meaning of the terms in a given model.

·         Knowledge of appropriate mathematical techniques to analyse the models.

·         Ability to make predictions.


Thus, the summative assessment for this module consists of:

·         One two-hour examination (80%)

·         One in-semester test at roughly the half way stage (20%).


Formative assessment and feedback

There will be 4 marked exercise sheets issued at roughly equal intervals. Written feedback is provided.

Reading list


Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.