Towards the control of networks with time-varying topologies: analysis of livestock trade

Dr. Philipp Hövel:

Many networks exhibit time-dependent topologies, where an edge only exists during a certain period of time or its weight is subject to temporal fluctuations and delays. This becomes of particular importance, if the evolution of the network topology operates on a timescale similar to the local dynamics of the nodes. Thus, time-varying networks form profound challenges for the control of the dynamics of coupled elements. While previous research has mostly focused on static or time-aggregated couplings, our objective is to develop a framework for the investigation of the dynamics on temporal networks.
This presentation addresses propagation properties of infectious diseases in time-dependent networks. In particular, we discuss the analysis of a dataset of livestock trade movements. The corresponding networks are known as a major route for the spread of animal diseases, where the chronology of contacts is crucial.
In detail, we find that a time-aggregated approach might fail to identify epidemiologically relevant nodes [1]. Hence, we explore the adaptability of the concept of centrality of nodes to temporal networks using a data-driven approach based on the example of animal trade. We utilize the size of the in- and out-component of nodes as centrality measures and show that a ranking of nodes according to their component sizes is reasonably stable for a wide range of infectious periods. Samples based on this ranking are robust enough against varying disease parameters and hence are promising tools for disease control. They could be used to identify sentinel nodes that are best suited to influence the dynamics on the networks.

[1] M. Konschake, H. H. K. Lentz, F. J. Conraths, P. Hövel, and T. Selhorst: "On the robustness of in- and out-components in a temporal graph", PLoS ONE 8, e55223 (2013).