Ashton, Stephen.pdf (5.31 MB)
The mathematics of human contact: developing stochastic algorithms for the generation of time-varying dynamic human contact networks
thesis
posted on 2023-06-09, 19:58 authored by Stephen AshtonIn this thesis, I provide a statistical analysis of high-resolution contact pattern data within primary and secondary schools as collected by the SocioPatterns collaboration. Students are graphically represented as nodes in a temporally evolving network, in which links represent proximity or interaction between students. I focus on link- and node-level statistics, such as the on- and off-durations of links as well as the activity potential of nodes and links. Parametric models are fitted to the onand off-durations of links, interevent times and node activity potentials and, based on these, I propose a number of theoretical models that are able to reproduce the collected data within varying levels of accuracy. By doing so, I aim to identify the minimal network-level properties that are needed to closely match the real-world data, with the aim of combining this contact pattern model with epidemic models in future work. I also provide Bayesian methods for parameter estimation using exact Bayesian and Markov Chain Monte Carlo methods, applying these in the case of Mittag-Leffler distributed data to artificially generated data and real-world examples. Additionally, I present probabilistic methods for model selection - namely the Akaike and Bayesian Information Criteria and apply them to the data and examples in the previous section.
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- Published version
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315.0Department affiliated with
- Mathematics Theses
Qualification level
- doctoral
Qualification name
- phd
Language
- eng
Institution
University of SussexFull text available
- Yes
Legacy Posted Date
2019-12-19Usage metrics
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