The mathematics of human contact: developing stochastic algorithms for the generation of time-varying dynamic human contact networks

In 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.