- Ken Eames
London School of Hygiene and Tropical Medicine, UK.
Title: Epidemics in humans: measuring and modelling contact patterns
Abstract: Social contact patterns are fundamental to understanding the spread of infectious diseases of humans. A number of different mathematical models have been developed that explicitly account for non-random mixing within a population. However, until recent years modelling efforts have been hampered by a lack of data describing relevant contact patterns. Recent studies, both high- and low-tech, have aimed to fill this gap. Here, we describe model development, social mixing data collection, and some of the problems that still remain to be solved.
- James Gleeson
MACSI, Department of Mathematics and Statistics, University of Limerick, Ireland.
Title: Approximation methods for contagion processes on complex networks
Abstract: A wide class of binary-state dynamics on complex networks that exhibit contagion—including, for example, the voter model, the Bass diffusion model, and the susceptible-infected-susceptible (SIS) disease spread model—can be described in terms of transition rates (spin-flip probabilities) that depend on the number of nearest neighbours in each of the two possible states. High-accuracy approximations for the emergent dynamics of such models on uncorrelated, infinite networks are given by recently-developed compartmental models or approximate master equations (AME). Pair approximations (PA) and mean-field theories can be systematically derived from the AME; we show that PA and AME solutions can coincide in certain circumstances. This facilitates bifurcation analysis, yielding explicit expressions for the critical (ferromagnetic/paramagnetic transition) point of such dynamics, closely analogous to the critical temperature of the Ising spin model.