The interaction of entities on a network structure is of significant importance to many disciplines. Network structures can have both physical (e.g. power grids, computer networks, the World Wide Web, networks of neurones) and non-physical (e.g. social networks of friends, links between communities, the movement of livestock) realisations that are all amenable to study. In this thesis work on dynamical processes and the networks on which they occur is presented from a viewpoint of both mathematical epidemiology and computational/theoretical neuroscience, with additional consideration of the intersection between the two. I begin with a paper illustrating how different models of disease transmission are derivable from others and provide a framework for the development of approximate ODEs based on their derivation from exact Kolmogorov equations. This work is followed with two papers that use two such approximate models and consider how they perform when the interplay between both disease and network dynamics is taken into account. Whilst the work in these papers focusses on the modelling of the temporal evolution of the disease and network dynamics, papers four and five consider the recent viewpoint within neuroscience that the brain operates within a critical regime. Making use of models analogous to meanfield models in epidemiology I analyse the behaviour of the system when it is in a balanced state, characterised by the system operating at or near its critical bifurcation, and how this is relevant to the brain itself. Whilst models used within the two areas are analogous, the behavioural aspects of interest within them are quite different. I conclude with a discussion of these differences, the overlaps between both fields and suggest where future work in each area may benefit from incorporating methods and ideas of the other.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:606046 |
| Date | January 2014 |
| Creators | Taylor, Timothy John |
| Publisher | University of Sussex |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://sro.sussex.ac.uk/id/eprint/48758/ |
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