Table 1.
The basic statistics of the data sets.
Fig 1.
The average outbreak size plotted against the basic reproduction number for 12 data sets (indicated in the Fig.) of human interaction.
Each point of the scatter plots corresponds to one pair (λ,δ), where λ is the infection probability and δ is the duration of infection. In the upper left corner there is a legend for the color-coding of these points. In the other panels, a data point is an average over 104 runs of the SIR model as described in the Methods section. The vertical lines mark R0 = 1—the epidemic threshold for the canonical, fully mixed SIR model.
Table 2.
Shape descriptors for the point clouds shown in Fig. 1.
Fig 2.
Explanation of shape descriptors to characterize the point clouds shown in Fig. 1.
All examples come from the Conference data set. Panel A describes Kendall’s τ—a correlation coefficient based on the counting of discordant pairs (pairs of points connected by a line of negative slope). Panels B and C show the maximal separation of discordant pairs. In B, the measures focus on the pair with the largest separation in the R0 direction. ΔR0 denotes the maximum separation; ρR0 is the mean R0 value for the maximally discordant pair. Panel C shows the similar quantities, ΔΩ and ρΩ, defined along the Ω direction. Panels D, E, and F illustrate the measurement of λδ-balance via ταΩ. This descriptor captures the tendency of some data sets to have high-λ, low-δ points above high-δ, low-λ points, while for other data sets, the situation is reversed. Panel D illustrates how the R0 axis is segmented into bins. Panel E shows how we assign a (λ,δ)-plane angle, α, to all points in the bin. Panel F shows how we measure the correlation between α and Ω, which is very weak in this particular case.
Table 3.
Descriptors of temporal network structure.
Fig 3.
Illustration of two descriptors of temporal network structure, fLC and FNT.
The measure illustrated in A and B, fLC, uses the order of the contact to separate the contacts; the measure in C and D, FNT, uses the real time. Panels A and C are time-line representations of a temporal network data set. Each horizontal line represents an individual. A contact between two individuals is indicated by a vertical arc. In A and B, we focus on the first contact between a pair of nodes. We measure the fraction of the number of node pairs that have been in direct contact when a fraction ν of the total number of contacts has been observed. This fraction is plotted against ν in B. The value at ν = 1/2 defines fLC. In the timeline (A) we highlight the first half contacts, which contribute to the calculation of fLC, in color and the first contact between each node pair by black contours. In panels C and D, we illustrate the calculation of FNT, which looks at nodes (rather than links) present in both the first and last time interval of width ϕ (measured as a fraction of the sampling time), shown in color in the timeline (C). The fraction of such nodes as a function of ϕ is graphed in D. FNT is defined as the value at ϕ = 0.05.
Fig 4.
The coefficient of determination R2 between the shape descriptors of the R0 vs. Ω point cloud and network descriptors.
The error bars are standard errors estimated by the jackknife resampling method. *: p < 0.05, **: p < 0.01, ***: p < 0.001.