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2005/06 Undergraduate Module Catalogue

MATH3564 Mathematical Biology

15 creditsClass Size: 100

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2005/06

Pre-requisites

MATH2360 or MATH2370 or MATH3501 or MATH3502, or equivalent.

This module is approved as an Elective

Objectives

This module aims to introduce the student to some areas of the biological sciences in which mathematics has a significant contribution to make, in order to model and understand a wide variety of biological phenomena. On completion of this module, students should be able to: (a) model, with understanding, a selected group of biological phenomena; (b) analyse the models using reaction-diffusion and phase-plane techniques; (c) determine the structure and stability of travelling waves; (d) determine biological patterns and their stability.

Syllabus

All the major developments in physical science and technology are underpinned by mathematics, both as a language for the concise statement of the laws of nature and as a tool for developing understanding of new phenomena by modelling analysis. The process of mathematisation is still at an early stage in biology, but it is becoming increasingly important in many areas. The analogue of technology here is medicine, the engineering of the living organism. This module aims to introduce the student to some of the areas of mathematical biology that are already well established but which are still giving rise to exciting new developments. Three topics will be taught from the following list: 1. Plankton Ecology Modelling the evolution of plankton populations, especially the interaction of phytoplankton (plant-like) and zooplankton (animal-like) populations. Sudden population bursts (blooms), oscillations. Links with world CO2 balance and fisheries production. 2. Nerve Physiology Modelling of unmyelinated nerve fibres leading to the Hodgkin-Huxley equations. Simplifications of FitzHugh and Nagumo and Piecewise linear caricatures. Travelling waves, threshold phenomena. Stability of waves. Modelling myelinated fibres.

3. Morphogenesis and Turing Instability Modelling morphogenes and pre-pattern through reaction-diffusion mechanisms. Turing instability analysis and its application to pattern formation. 4. Reaction-Diffusion Models Study of maximum and comparison principles for scalar equations, travelling waves and stability using examples from population genetics (Fisher?s equations and Nagumo?s equation). 5. Tumour Growth Modelling the growth of solid tumours. The processes of angiogenesis, vascularisation and metastasis. The role of chemotaxis. 6. Chemical Reactions and Biological Clocks Mass-Action laws, modelling Belousov-Zhabotinsky reaction and autocatalytic processes. The analogy with Biological clocks and Circadium rhythms.

Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures: 26 hours. 7 examples classes.

Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

One 3 hour examination at end of semester (100%).

Reading list

The reading list is available from the Library website

Last updated: 13/05/2005

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