Spatiotemporal Activity-Driven Networks

TL;DR

This paper introduces a spatial activity-driven network model that incorporates spatial constraints, enabling analytical study of how space influences network dynamics, clustering, and spreading processes, with applications to social distancing strategies.

Contribution

The paper presents a novel, analytically tractable spatiotemporal contact network model that captures the effects of space on network structure and dynamics, extending the activity-driven framework.

Findings

Model reproduces social network features like clustering and strong/weak ties.

Spatial constraints slow down spreading dynamics.

Targeted spatial interventions effectively reduce long-range contacts.

Abstract

Temporal-network models have provided key insights into how time-varying connectivity shapes dynamical processes such as spreading. Among them, the activity-driven model is a widely used, analytically tractable benchmark. Yet many temporal networks, such as those of physical proximity, are also embedded in space, and spatial constraints are known to affect dynamics unfolding on the networks strongly. Despite this, there is a lack of similar simple and solvable models for spatiotemporal contact structures. Here, we introduce a spatial activity-driven model in which short-range contacts are more frequent. This model is analytically tractable and captures the joint effects of space and time. We show analytically and numerically that the model reproduces several characteristic features of social and contact networks, including strong and weak ties, clustering, and triangles having weights above the median. These traits can be attributed to space acting as a form of memory. Simulations of spreading dynamics on top of the model networks further illustrate the role of space, highlighting how localisation slows down spreading. Furthermore, the framework is well-suited for modelling social distancing in a principled way as an intervention measure aimed at reducing long-range links. We find that, unlike for non-spatial networks, even a small spatially targeted reduction in the total number of contacts can be very effective. More broadly, by offering a tractable framework, the model enables systematic exploration of dynamical processes on spatiotemporal networks.