SM-4341 Mathematical Biology
Module Code
:
SM-4341
Module Title
:
Mathematical Biology
Type of Module :
Optional
Modular Credits :
4
Student Workload :
Contact hours for
timetabling
:
Prerequisite
:
SM-4312 Mathematical Modelling
Anti-requisite
Aims:
:
None
8 - 10 hours/week
4 hours / week
This module continues the study of the application of mathematical techniques to realworld problems introduced in SM-4312 Mathematical Modelling, and is intended for
students who are either majoring in Biomathematics or are majoring in Applied
Mathematics and are interested in specialising in biological modelling.
The central theme of the module is the use of partial differential equations in describing
and predicting the behahiour of biological systems.
Module Content:
1. Reaction diffusion, chemotaxis and non-local mechanisms (simple random walk
derivation of the diffusion equation, reaction diffusion equations, models for insect
dispersal and chemotaxis).
2. Oscillator generated wave phenomena and central pattern generators (kinematic waves
in the Belousov-Zhabotinskii reaction, central pattern generator)
3. Single species models (travelling wave, Fisher equation, asymptotic solutions and
stability of wavefront solutions, density-dependent reaction diffusion equations and exact
solutions, waves in models with multi-steady state kinetics - the spread and control of an
insect population, calcium waves on Amphibian eggs)
4. Multi-species reaction diffusion models (waves of pursuit and evasion in predator-prey
systems, travelling fronts in the Belousov-Zhabotinskii reaction, waves in excitable media,
travelling wave trains with oscillatory kinetics)
5. Spatial pattern formation with reaction/population interaction diffusion mechanisms
(role of pattern in developmental biology; Turing mechanisms; pattern initiation in a
reaction diffusion mechanism; Dispersion relation, Turing space, scale and geometry
effects in pattern formation in morphogenetic models).
Assessment:
Examination:60%
Course Work:40%
(2 class tests, 20% each)