Contagion on Networks with Self-Organised Community Structure

Living systems are organised in space. This imposes constraints on both their structural form and, consequently, their dynamics. While artificial life research has demonstrated that embedding an adaptive system in space tends to have a significant impact on its behaviour, we do not yet have a full account of the relevance of spatiality to living self-organisation. Here, we extend the REDS model of spatial networks with self-organised community structure to include the "small world" effect. We demonstrate that REDS networks can become small worlds with the introduction of a small amount of random rewiring. We then explore how this rewiring influences two simple dynamic processes representing the contagious spread of infection or information. We show that epidemic outbreaks arise more easily and spread faster on REDS networks compared to standard random geometric graphs (RGGs). Outbreaks spread even faster on small world REDS networks (due to their shorter path lengths) but initially find it more difficult to establish themselves (due to their reduced community structure). Overall, we find that small world REDS networks, with their combination of short characteristic path length, positive assortativity, strong community structure and high clustering, are more susceptible to a range of contagion dynamics than RGGs, and that they offer a useful abstract model for studying dynamics on spatially organised living systems.