Module code: MAT3040

Module Overview

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

Module provider

Mathematics & Physics

Module Leader

DERKS Gianne (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 6

Module cap (Maximum number of students): N/A

Overall student workload

Independent Learning Hours: 84

Lecture Hours: 33

Captured Content: 33

Module Availability

Semester 2

Prerequisites / Co-requisites

MAT2007 Ordinary Differential Equations

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.  

Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test In-semester test (50 min) 20
Examination Exam (2 hrs) 80

Alternative Assessment


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 (20%).


Formative assessment and feedback

There will be marked exercise sheets. Written feedback is provided.

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
1 An understanding of how to model ecological and epidemiological problems using differential equations (ordinary, partial and delay) KCT
2 An understanding of appropriate analytical techniques for the study of such problems KC
3 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

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.


Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list
Upon accessing the reading list, please search for the module using the module code: MAT3040

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 2022/3 academic year.