Spatiotemporal activity-driven networks

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 localization slows down spreading. Furthermore, the framework is well suited for modeling social distancing in a principled way as an intervention measure aimed at reducing long-range links. We find that, unlike for nonspatial 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.