Social encounter networks: collective properties and disease transmission

Abstract

A fundamental challenge of modern infectious disease epidemiology is to quantify the networks of social and physical contacts through which transmission can occur. Understanding the collective properties of these interactions is critical for both accurate prediction of the spread of infection and determining optimal control measures. However, even the basic properties of such networks are poorly quantified, forcing predictions to be made based on strong assumptions concerning network structure. Here, we report on the results of a large-scale survey of social encounters mainly conducted in Great Britain. First, we characterize the distribution of contacts, which possesses a lognormal body and a power-law tail with an exponent of -2.45; we provide a plausible mechanistic model that captures this form. Analysis of the high level of local clustering of contacts reveals additional structure within the network, implying that social contacts are degree assortative. Finally, we describe the epidemiological implications of this local network structure: these contradict the usual predictions from networks with heavy-tailed degree distributions and contain public-health messages about control. Our findings help us to determine the types of realistic network structure that should be assumed in future population level studies of infection transmission, leading to better interpretations of epidemiological data and more appropriate policy decisions.

Figure 1.

Capturing individual contact heterogeneity. (a) Examples of ego-centric networks collected by the survey. From left to right: school pupil, female aged 12 years; flight attendant, female 22; fire fighter, male 44; retired, male 62. The participant (ego) is the orange central triangle; circles represent individual contacts, and squares represent groups of contacts (size of group indicated). Colours represent social settings of encounters (red, home; blue, work/school; yellow, travel; green, other). Larger symbol sizes represent longer contact durations, while a closer proximity to the ego indicates the contact is more frequently encountered. (b) The distribution of contacts (node degree) from the survey with no group information included (red squares) and with groups included (black circles). (c) The distribution of the number of contacts (node degree) from the survey (open circles), compared with our model of daily contacts (red line; see electronic supplementary material), and a guide to the eye line following a power-law decay with exponent of −2.45. Confidence intervals of the distribution are determined by bootstrapping (open circles, with groups; red line with dots, model; blue dashed line, dPlN fit; dashed-dotted line, slope =−2.4).

Figure 2.

Local clustering of contacts. (a) Relationship between number of contacts reported, , and the clustering between those contacts (red, unweighted; blue, weighted); confidence intervals are determined by bootstrapping. (b,c) Transitive matrices showing the degree of clustering stratified by social context and distance from home; the values are the proportion of transitive links between contacts in different setting compared with the theoretical maximum.

Figure 3.

Epidemiological implications of local network structure: three network models are compared: a simple (unweighted, unclustered) network (shown in red), a weighted network accounting for duration of contact (green) and a clustered weighted static network accounting for the full structure around participant (blue). (a) Distributions of the number of secondary cases (R_i) for the four examples in figure 1a. (b) Distribution of secondary cases across the entire sample of participants (R_i). (c) Distribution of expected number of secondary cases per participant (). We have modelled a short-lived, rapidly transmitted infection, with a latent period of 3 days, an infectious period of 3 days (), and a transmission rate, τ, of 0.1 h^{− 1} across a network connection.