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Module Descriptors

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Session: 2022/23

Last modified: 15/07/2021 12:05:56

Title of Module: Mathematical Biology

Code: MATH10010 SCQF Level: 10
(Scottish Credit and Qualifications Framework)		 Credit Points: 20 ECTS: 10
(European Credit Transfer Scheme)
School:School of Computing, Engineering and Physical Sciences
Module Co-ordinator:Alan  J.  Walker

Summary of Module

The module covers the mathematical modelling of biological phenomena.

Students will begin to understand why ordinary differential equations (ODEs) can arise in modelling biological phenomena. One-dimensional autonomous ODEs will be covered, including a treaty on equilibrium points, stability, phase plots, and linear stability analysis within the context of mathematical biology.

These ideas will be expanded to consider systems of two or more ODEs, paying attention to equilibria and the stability thereof, phase plane analysis, and linear stability analysis, within the context of interacting species and/or disease modelling.

Biological movement and pattern formation will be introduced, with mention made to chemical diffusion, chemotaxis, reaction-diffusion equations, Turing patterns and diffusion-driven instability.

Travelling waves will be touched upon, with regard to Fisher’s equation, wound healing and epidemiology. Further, the modelling of infectious diseases will be covered, with an introduction to SIR models, the Kermack-McKenzie model, steady-states and linear stability.

Reaction kinetics will be studied, including the Law of Mass Action, enzyme reactions, the pseudo steady-state hypothesis, and singular perturbation techniques.

Finally, discrete time population models will be introduced, via difference equations models for seasonally reproducing organisms, harvesting, obtaining maximum sustainable yields, Leslie matrices and the Jury conditions for stability.

The Graduate Attributes relevant to this module are given below:

  • Academic: Critical thinker; Analytical; Inquiring; Knowledgeable; Problem-solver; Digitally literate; Autonomous.
  • Personal: Motivated, Creative; Resilient.
  • Professional: Research-minded; Ambitious; Driven.

Module Delivery Method
Face-To-FaceBlendedFully OnlineHybridCHybridOWork-based Learning
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Face-To-Face
Term used to describe the traditional classroom environment where the students and the lecturer meet synchronously in the same room for the whole provision.

Blended
A mode of delivery of a module or a programme that involves online and face-to-face delivery of learning, teaching and assessment activities, student support and feedback. A programme may be considered “blended” if it includes a combination of face-to-face, online and blended modules. If an online programme has any compulsory face-to-face and campus elements it must be described as blended with clearly articulated delivery information to manage student expectations

Fully Online
Instruction that is solely delivered by web-based or internet-based technologies. This term is used to describe the previously used terms distance learning and e learning.

HybridC
Online with mandatory face-to-face learning on Campus

HybridO
Online with optional face-to-face learning on Campus

Work-based Learning
Learning activities where the main location for the learning experience is in the workplace.


Campus(es) for Module Delivery
The module will normally be offered on the following campuses / or by Distance/Online Learning: (Provided viable student numbers permit)
Paisley:Ayr:Dumfries:Lanarkshire:London:Distance/Online Learning:Other:
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Term(s) for Module Delivery
(Provided viable student numbers permit).
Term 1

 

Term 2

 

Term 3

 

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Learning Outcomes: (maximum of 5 statements)

On successful completion of this module the student will be able to:

L1. Demonstrate detailed knowledge and understanding of equilibria and stability in ODE models of biological phenomena.

L2. Demonstrate detailed knowledge and understanding of the mathematics involved in biological movement and pattern formation.

L3. Demonstrate detailed knowledge and understanding of mathematical modelling of reaction kinetics.

L4. Demonstrate detailed knowledge and understanding of discrete time population models.

Employability Skills and Personal Development Planning (PDP) Skills
SCQF Headings During completion of this module, there will be an opportunity to achieve core skills in:
Knowledge and Understanding (K and U) SCQF Level 10.

Demonstrating a detailed knowledge and understanding of important techniques used in creating and analysing models which arise in biological phenomena.

Demonstrating critical awareness of established techniques of enquiry in common biological applications of differential equations and difference equations.

Practice: Applied Knowledge and Understanding SCQF Level 10.

Using a range of standard techniques to analyse and solve problems at advanced levels, and sometimes in non-routine contexts.

Carrying out defined investigative problems within a mathematically based subject.

Generic Cognitive skills SCQF Level 10.

Conceptualising and analysing problems informed by professional and research issues.

Communication, ICT and Numeracy Skills SCQF Level 10.

Making formal written presentation(s) based on the output from an investigative problem.

Autonomy, Accountability and Working with others SCQF Level 10.

Exercising independence and initiative in carrying out complex activities.

Identifying learning needs through reflection based on self, tutor and peer evaluation of work.

Pre-requisites: Before undertaking this module the student should have undertaken the following:
Module Code:
MATH09002
Module Title:
Advanced Calculus
Other:or equivalent.
Co-requisitesModule Code:
Module Title:

* Indicates that module descriptor is not published.

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Learning and Teaching
Learning Activities
During completion of this module, the learning activities undertaken to achieve the module learning outcomes are stated below: 		Student Learning Hours
(Normally totalling 200 hours):
(Note: Learning hours include both contact hours and hours spent on other learning activities)
Lecture/Core Content Delivery36
Tutorial/Synchronous Support Activity12
Independent Study152
200 Hours Total

**Indicative Resources: (eg. Core text, journals, internet access)

The following materials form essential underpinning for the module content and ultimately for the learning outcomes:

“Mathematical Biology” class notes as published on the University VLE.

"Mathematical Biology", J D Murray, 3rd Edition.

“Essential Mathematical Biology”, N Britton, 1st Edition.

“Mathematical Aspects of Reacting and Diffusing Systems”, P C Fife, 1st Edition.

(**N.B. Although reading lists should include current publications, students are advised (particularly for material marked with an asterisk*) to wait until the start of session for confirmation of the most up-to-date material)

Engagement Requirements

In line with the Academic Engagement Procedure, Students are defined as academically engaged if they are regularly engaged with timetabled teaching sessions, course-related learning resources including those in the Library and on the relevant learning platform, and complete assessments and submit these on time. Please refer to the Academic Engagement Procedure at the following link: Academic engagement procedure

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Supplemental Information

Programme BoardPhysical Sciences
Assessment Results (Pass/Fail) No
Subject PanelPhysical Sciences
ModeratorDr Kenneth C Nisbet
External ExaminerC Macdonald
Accreditation Details
Version Number

1.01

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Assessment: (also refer to Assessment Outcomes Grids below)
Assignment: an individual coursework task, 20% of the final mark,
Examination: a final, closed book assessment, 80% of the final mark
(N.B. (i) Assessment Outcomes Grids for the module (one for each component) can be found below which clearly demonstrate how the learning outcomes of the module will be assessed.
(ii) An indicative schedule listing approximate times within the academic calendar when assessment is likely to feature will be provided within the Student Handbook.)

Assessment Outcome Grids (Footnote A.)

Component 1
Assessment Type (Footnote B.) Learning Outcome (1) Learning Outcome (2) Learning Outcome (3) Learning Outcome (4) Weighting (%) of Assessment ElementTimetabled Contact Hours
Unseen closed book (standard)check markcheck markcheck markcheck mark802

Component 2
Assessment Type (Footnote B.) Learning Outcome (1) Learning Outcome (2) Learning Outcome (3) Learning Outcome (4) Weighting (%) of Assessment ElementTimetabled Contact Hours
Class test (practical)check mark   206
Combined Total For All Components100% 8 hours

Footnotes
A. Referred to within Assessment Section above
B. Identified in the Learning Outcome Section above

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Note(s):
  1. More than one assessment method can be used to assess individual learning outcomes.
  2. Schools are responsible for determining student contact hours. Please refer to University Policy on contact hours (extract contained within section 10 of the Module Descriptor guidance note).
    This will normally be variable across Schools, dependent on Programmes &/or Professional requirements.

Equality and Diversity
The module is suitable for any student satisfying the pre-requisites.
UWS Equality and Diversity Policy
(N.B. Every effort will be made by the University to accommodate any equality and diversity issues brought to the attention of the School)

2014 University of the West of Scotland

University of the West of Scotland is a Registered Scottish Charity.

Charity number SC002520.

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