Temporal network structures controlling disease spreading

We investigate disease spreading on eight empirical data sets of human contacts (mostly proximity networks recording who is close to whom, at what time). We compare three levels of representations of these data sets: temporal networks, static networks, and a fully connected topology. We notice that the difference between the static and fully connected networks—with respect to time to extinction and average outbreak size—is smaller than between the temporal and static topologies. This suggests that, for these data sets, temporal structures influence disease spreading more than static-network structures. To explain the details in the differences between the representations, we use 32 network measures. This study concurs that long-time temporal structures, like the turnover of nodes and links, are the most important for the spreading dynamics.

Figure 1

A visualization of the temporal structures of the data sets. The nodes are represented by a coordinate of the vertical axis. A contact at a certain time is displayed as a horizontal line between the coordinates of the nodes involved. The assignment of coordinates is optimized to reduce the total vertical distance of the lines.

Figure 2

The network structure of the networks of aggregate contacts displayed using the “Force Atlas 2” method of the software package gephi (gephi.org).

Figure 3

Average extinction times for the SIR model on eight temporal-network data sets of human proximity.

Figure 4

The difference between the average time to extinction of static- and temporal-network representations of the contact patterns.

Figure 5

The difference between the average time to extinction of fully mixed and temporal-network representations of the contact patterns.

Figure 6

Average outbreak sizes for the SIR model on eight temporal-network data sets of human proximity.

Figure 7

The difference between the average outbreak size of static- and temporal-network representations of the contact patterns.

Figure 8

The difference between the average outbreak size of fully mixed and temporal-network representations of the contact patterns.

Figure 9

(a) The top three temporal-network structures separating the Prostitution, Gallery 1, and Gallery 2 data sets from the rest of the data sets and (b) separating Prostitution from the rest. $x$ is the difference between the smallest value (of the network structural measure in question) of the set containing the largest value, and the largest value of the other set divided by the difference between the largest and smallest values in the union of the sets.