Mathematical Biology II module (MA42002)

About the module

The aim of this module is to introduce Level 4 students to some biological phenomena and their formulation in terms of mathematical models, building on the work in MA32009/MA41002 (Mathematical Biology I). This module is mandatory for Level 4 students taking the BSc or MSci in Mathematical Biology, and may optionally be taken in combination with other modules by students taking the BSc or MMath in Mathematics or any of the other Mathematics combined degrees. If you have questions about this module or the possible combinations, please contact your Advisor of Studies.

Prerequisites

Students taking this module must have achieved a pass mark in the module MA32009, or in MA41002, or equivalent.

Indicative Content

• Modelling of Biological Systems using Partial Differential Equations

  Derivation of conservation equations. Different models for movement (e.g. diffusion, convection, directed movement). Connection between diffusion and probability.

• Linear reaction-diffusion equations

  Fundamental solution for linear diffusion equations. Speed of a wave of invasion.

• Non-linear reaction-diffusion equations

  Travelling wave solutions for monostable equations (e.g. Fisher equation). Travelling wave solutions for bistable equations.

• Systems of reaction-diffusion equations

  Travelling wave solutions for systems of reaction-diffusion equations. Pattern formations in systems of reaction-diffusion equations. Pattern formations in chemotaxis equations.

• Mathematical modelling of infection diseases (SIR)

  Derivation of a simple SIR model. Travelling wave solutions for the simple SIR model. Generalisation of the simple SIR model. Stochastic SIR model.

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (80%) and coursework (20%).

Credit Rating

This module is a Scottish Higher Education Level 4 or SCQF level 10 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.