The Mathematics of Human Contact: Developing a Model for Social Interaction in School Children

TL;DR

This paper analyzes high-resolution contact data among school children, modeling their interactions as dynamic networks to understand contact patterns and develop theoretical models for epidemic simulations.

Contribution

It introduces a statistical analysis and parametric models of contact patterns in school settings, identifying minimal network properties for realistic modeling.

Findings

Parametric models fit on- and off-durations of links and node activity potentials.

The models can reproduce real contact data with varying accuracy.

Insights into minimal network properties needed for accurate epidemic modeling.

Abstract

In this paper, we 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. This article focuses 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 on- and off-durations of links, inter-event times and node activity potentials and, based on these, we propose a number of theoretical models that are able to reproduce the collected data within varying levels of accuracy. By doing so, we 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.