MacDonald, MacDonald, James I. (2007) A computational investigation of seasonally forced disease dynamics. PhD thesis, University of Warwick.

Preview	Text WRAP_THESIS_MacDonald_2007.pdf - Submitted Version Download (8Mb) | Preview
	Other (Permission email) Permission email - McDonald.msg - Other Embargoed item. Restricted access to Repository staff only Download (61Kb)

Request Changes to record.

Abstract

In recent years there has been a great increase in work on epidemiological
modelling, driven partly by the increase in the availability and power of
computers, but also by the desire to improve standards of public and animal
health. Through modelling, understanding of the mechanisms of previous
epidemics can be gained, and the lessons learnt applied to make predictions
about future epidemics, or emerging diseases.
The standard SIR model is in some sense quite a simplistic model, and
can lack realism. One solution to this problem is to increase the complexity of
the model, or to perform full scale simulation—an experiment in silico. This
thesis, however, takes a different approach and makes an in depth analysis
of one small improvement to the model: the replacement of a constant birth
rate with a birth pulse. This more accurately describes the seasonal birth
patterns observed in many animal populations. The combination of the
nonlinearities of the SIR model and the strong seasonal forcing provided
by the birth pulse necessitate the use of numerical methods. The model
shows complex multi annual cycles of epidemics and even chaos for shorter
infectious periods.
The robustness of these results are proven with respect to a wide range
or perturbations: in phase space, in the shape and temporal extent of the
birth pulse and in the underlying model to which the pulsing is applied.
To complement the numerics, analytic methods are used to gain further
understanding of the dynamics in particular areas of the chosen parameter
space where the numerics can be challenging. Three approximations are
presented, one to investigate very small levels of forcing, and two covering
short infectious periods.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics R Medicine > RA Public aspects of medicine
Library of Congress Subject Headings (LCSH):	Communicable diseases -- Epidemiology -- Mathematical models, Immune response -- Mathematical models, Diseases -- Seasonal variations -- Mathematical models
Official Date:	July 2007
Dates:	Date Event July 2007 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Keeling, Matthew James
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC)
Extent:	xiv, 186 leaves
Language:	eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item