Course Details in

Module Title	LM Mathematical Biology II
School	Mathematics
Department	Mathematics
Module Code	06 27690
Module Lead	Dr Rosemary Dyson
Level	Masters Level
Credits	10
Semester	Semester 2
Pre-requisites	LI Differential Equations - (06 25670) LI Multivariable & Vector Analysis - (06 25667)
Co-requisites
Restrictions	None
Contact Hours	Lecture-18 hours Practical Classes and workshops-9 hours Guided independent study-73 hours Total: 100 hours
Exclusions
Description	In many biological systems, the concentrations of proteins, metabolites and other objects of study, are spatially-varying. Diffusion (‘spreading out’), and potentially also advection (‘movement due to flow’) or taxis (‘guided movement’) then become important. Mathematical models of reaction-diffusion and advection-reaction-diffusion systems are given by systems of partial differential equations. This module will introduce some paradigm models, techniques for their analysis and solution, and the types of phenomena that can be predicted and/or explained when spatial variation and transport are considered. Topics to be covered include: autocatalytic reaction-diffusion waves, spread of epidemics, bioreactors, nerve signal transmission, Turing patterns and animal coat markings.
Learning Outcomes	By the end of the module students should be able to: Formulate models of biological systems involving spatial variation, e.g. nerve signal transmission, tumour growth, animal coat markings, and applications in cell culture. Formulate both reaction-diffusion and advection-reaction-diffusion models. Analyse, simplify, and in some cases solve the resulting PDE systems. Methods to be used include travelling wave solutions, free boundary problems and finding conditions for the onset of the instabilities associated with pattern formation. Use models to make biologically-interpretable predictions and use these to critically assess and refine the model to the given situation.
Assessment	27690-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions	Assessment: 75% on a 1.5 hour examination; 25% from coursework (miniproject, computer laboratories, problem sheets) Reassessment: 100% on a 1.5 hour resit examination.
Other
Reading List