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MA30358: Mathematical biology: biomedical applications

[Page last updated: 22 May 2025]

Academic Year: 2025/26
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 2
Assessment Summary: EXOB 100%
Assessment Detail:
  • MA32058 Open-book written examination (EXOB 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA22016 OR take MA22034 OR take MA20223
Before taking this module you are advised to take MA22035 AND take MA22021
In taking this module you cannot take MA30063
Learning Outcomes:
* Derive and interpret mathematical models of biological systems using PDEs.
* Discuss and apply mathematical methods to analyse PDE models of biological systems.
* Give a qualitative and quantitative of the behaviour of PDE models for biological systems.
* Interpret the mathematical analysis in terms of the original biological context.


Synopsis: In this unit you will explore the use of partial differential equations to model and understand biological systems. You will study how to formulate, analyse and interpret appropriate mathematical models to examine biomedical processes and phenomena. This unit will give you the chance to extend your knowledge of mathematical modelling, develop your understanding of theoretical biology, and encounter a broader range of biological applications.

Content: Biological motion: derivation of conservation equation (macroscopic approach); derivation of diffusion-advection equation (microscopic approach); components of flux (diffusion, advection, chemotaxis); solution of advection equation by characteristics; solutions of diffusion equation using the fundamental solution; steady state distributions; transit times. Spatial pattern formation: critical domain size; scale and geometry effects; Turing mechanisms; dispersion relation and Turing space. Tumour Growth - formation of necrotic core; tumour size. Computational approaches.

Course availability:

MA30358 is Optional on the following courses:

Department of Mathematical Sciences
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes:

  • This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
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