The implications of network structure for epidemic dynamics

The differences between mass-action and network-based models are investigated to determine when mass- action models are a reliable tool, and suggest ways in which their behaviour should be refined.

Abstract

It has long been realised that the standard assumptions of mass-action mixing are a crude approximation of the true mechanistic processes that govern the transmission of infection. In particular, many infections can be considered to be spread through a limited network of contacts. Yet, despite the underlying discrepancies, mass-action models continue to be used and provide a remarkably accurate description of epidemic behaviour. Here, the differences between mass-action and network-based models are investigated. This allows us to determine when mass-action models are a reliable tool, and suggest ways in which their behaviour should be refined.