MA4N4-15 Transport Processes in Mathematical Biology
Introductory description
Biological systems are seldom well-mixed, but rather have spatial variations. In such cases, it is important to consider transport processes within the system, for instance in the spread of an invasive species, the swimming of bacteria towards nutrients, or the morphogenesis of a tiger's stripes. This module will cover the main mathematical techniques for modelling biological systems with transport, and will be focused around systems of coupled advection-diffusion-reaction partial differential equations, as well as agent-based equations.
Module aims
The aims of this module are:
- To develop and understand a range of models for transport processes in biology.
- To articulate commonality in these models across systems, and elucidate their differences.
- Develop the partial differential equations relating to agent-based transport models, understanding when these are valid.
- Quantify a range of wave-like and self-similar transport behaviours displayed in various biological systems.
- Understand spatial pattern formation and diffusion-driven instability.
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.
- Reynold's Transport Theorem, flux, and dimensionless quantities.
- From agent-based models to transport PDEs.
- Biological waves in single and two-species models.
- Invasive species.
- Spatial pattern formation.
Learning outcomes
By the end of the module, students should be able to:
- Derive transport PDEs from agent-based models.
- Find travelling wave solutions to single- and multi-species population models.
- Find solutions to invasive species problems in different domains.
- Quantify the relative importance/speed of transport processes in a given biological system.
- Find the conditions for a Turing Instability to occur in a system.
Interdisciplinary
This is a mathematics focused module on the life science interface. Students will be taught the necessary biology.
Subject specific skills
Ability to translate biological mechanisms into mathematical framework, eg growth in algal bioreactors
Ability to analyse wave-like solutions of coupled PDEs representing biological processes.
Ability to derive conditions for pattern formation in coupled PDE systems.
Transferable skills
Ability to translate scientific ideas into mathematical language and back. Ability to think creatively. Ability to discern the validity of a proposed explanation.
Study time
Type | Required |
---|---|
Lectures | 30 sessions of 1 hour (29%) |
Seminars | 9 sessions of 1 hour (9%) |
Private study | 66 hours (63%) |
Total | 105 hours |
Private study description
Homework problems.
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Assessment group B1
Weighting | Study time | Eligible for self-certification | |
---|---|---|---|
Assessment component |
|||
In-person Examination | 100% | 45 hours | No |
Standard 3 hour written exam.
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Reassessment component is the same |
Feedback on assessment
Written feedback on the outcome of the exam.
Courses
This module is Optional for:
- Year 1 of TMAA-G1P0 Postgraduate Taught Mathematics
-
TMAA-G1PC Postgraduate Taught Mathematics (Diploma plus MSc)
- Year 1 of G1PC Mathematics (Diploma plus MSc)
- Year 2 of G1PC Mathematics (Diploma plus MSc)
This module is Option list A for:
- Year 4 of UPXA-FG31 Undergraduate Mathematics and Physics (MMathPhys)
This module is Option list B for:
- Year 1 of TPXA-F345 Postgraduate Taught Modelling of Heterogeneous Systems (PGDip)
- Year 4 of UCSA-G4G3 Undergraduate Discrete Mathematics
- Year 5 of UCSA-G4G4 Undergraduate Discrete Mathematics (with Intercalated Year)
This module is Option list C for:
-
UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
- Year 4 of G105 Mathematics (MMath) with Intercalated Year
- Year 5 of G105 Mathematics (MMath) with Intercalated Year
-
UMAA-G103 Undergraduate Mathematics (MMath)
- Year 3 of G103 Mathematics (MMath)
- Year 4 of G103 Mathematics (MMath)
- Year 4 of UMAA-G107 Undergraduate Mathematics (MMath) with Study Abroad