Applied Maths Honours Seminar

The order of presentations of this year’s Applied Maths Honours Students is as follows:

2.00 to 2.30    Prudence Philp
2.30 to 3.00    Shannon He
3.00 to 3.30    Angus Liu
3.30 to 4.00    Dhruv Saxena

*** 
Time: 2.00 to 2.30 
Speaker: Prudence Philp 
Title: Modelling the effects of vaccination in populations 

Abstract: Vaccination causes changes in the dynamics of disease in a population.  I will
use a simple disease model to derive some effects of introducing an infant vaccine into
a population.  Some of these effects are not ideal, and more realistic modelling can
show that for some diseases, vaccinating below threshold levels can have perverse
consequences for the population.  

Many childhood diseases are characterised by seasonal fluctuations.  Modelling
seasonality is important for developing vaccination schemes since periodic behaviour can
be exploited by vaccinating in pulses.  I will discuss some of the implications of
including seasonality in models, specifically focussing on recent attempts at using the
same disease model to explain several seasonal childhood diseases with widely different
patterns of behaviour.  

*** 
Time: 2.30 to 3.00 
Speaker: Shannon He 
Title: Cellular Automata Modelling of HIV Infection 

Abstract: The dynamics of the long-lasting, latent phase of the three-stage HIV-1
infection is not well understood even to this day.  Many theories have been proposed to
explain the phenomenon, one of which is the notion of deceptive imprinting, or original
antigenic sin.  The essence of this idea is that immune cells produced in response to an
initial viral infection may in fact suppress the creation of new immune cells in
response to newly evolved viral strains.  Hence a chronic infection that involves viral
strains capable of undergoing point mutations cannot be easily overcome as the immune
system fails to create new immune cells promptly.  We incorporate this idea of immune
competition in a Cellular Automata (CA) model and investigate its impact on the dynamics
of both the viral and immune system.  Our findings are presented with reference to
previous work.  

*** 
Time: 3.00 to 3.30 
Speaker: Angus Liu 
Title: Chaos in the Solar System - a study of the motion of Pluto 

Abstract: When Newton formulated the laws of gravitation and motion in the 17th Century,
it was thought that all physical phenomena could be entirely predicted, given that at
some instant we knew the position and motion of all the particles in the universe.
Nowhere was this more evident than in the clockwork-like motions of the planets and
other bodies in our Solar System.  In 1988, two theorists from MIT, Sussman and Wisdom
showed with accurate numerical schemes that the motion of Pluto was in fact chaotic with
a predictable timescale of only around 200 million years.  This came as a great shock,
with the further consequence that the chaotic motion of Pluto could cause chaotic motion
in the other planets due to its gravitational perturbations, and so the whole solar
system could be ultimately chaotic.  

*** 
Time: 3.30 to 4.00 
Speaker: Dhruv Saxena 
Title: Level Set Method for surface minimisation 

Abstract: Periodic minimal surfaces are ubiquitous in nature, many of them occuring
within cell membranes and intercellular structures.  In order to study them numerically,
it is necessary to have an effective method for constructing and analysing minimal
surfaces.  In this study we use a level set approach to model the Schwartz P surface in
terms of Fourier series.  We derive the differential equations for the Fourier
coefficients, from which the minimal surface is constructed.  The talk will introduce
ideas from Level Set Theory and discuss the results of this new approach.