Estimating within-school contact networks to understand influenza transmission

Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an open area of exploration. We develop a detailed statistical model to estimate the social contact network within a high school using friendship network data and a survey of contact behavior. Our contact network model includes classroom structure, longer durations of contacts to friends than nonfriends and more frequent contacts with friends, based on reports in the contact survey. We performed simulation studies to explore which network structures are relevant to influenza transmission. These studies yield two key findings. First, we found that the friendship network structure important to the transmission process can be adequately represented by a dyad-independent exponential random graph model (ERGM). This means that individual-level sampled data is sufficient to characterize the entire friendship network. Second, we found that contact behavior was adequately represented by a static rather than dynamic contact network.

💡 Research Summary

This paper addresses a critical gap in infectious‑disease modeling: the reliance on the simplifying assumption of random mixing within predefined groups (households, schools, workplaces) despite abundant evidence that real social contact patterns are highly structured. The authors develop a comprehensive statistical framework to infer the within‑school contact network of a large high‑school population by integrating two data sources: (1) a friendship network derived from the Add Health study, which records up to five male and five female friends for each student, and (2) a detailed contact‑behavior survey administered in two Virginia high schools that captures the average number of contacts during class breaks, lunch, and the proportion of contacts that occur with friends.

The first step is to model the friendship network itself. Using the observed dyadic ties, the authors fit a dyad‑independent exponential random graph model (ERGM). In this specification, the probability of an edge between any two students depends only on node‑level covariates (grade, gender, class size) and not on the presence of other edges. The fitted ERGM reproduces the empirical degree distribution, clustering coefficient, and other global statistics, demonstrating that individual‑level attributes are sufficient to capture the overall friendship structure without needing to observe the full network.

Next, the contact‑behavior survey is used to estimate the distribution of daily contact counts (the “degree” of the contact network). Because the reported means and variances exhibit over‑dispersion, the authors employ negative‑binomial regression models. The number of break‑time contacts is modeled as a function of the number of friends, yielding an estimated multiplicative increase of 1.03 in expected contacts per additional friend. Lunch‑time contacts, by contrast, show no significant dependence on friend count and are modeled with a simple negative‑binomial distribution. Outliers are truncated (e.g., >20 break contacts, >30 lunch contacts) and treated as censored observations.

With the friendship ERGM and the estimated degree distributions in hand, the authors construct a synthetic daily contact network. They define a “contact” as a 10‑minute face‑to‑face interaction; thus, an hour of shared time corresponds to six contacts, and a maximum of 38 contacts per dyad per day is allowed (reflecting a 6‑hour school day). The network is built conditional on the friendship graph: edges between friends receive higher contact probabilities and longer expected durations, while non‑friends in the same classroom receive lower probabilities. Classroom schedules (seven 40‑minute periods, a 50‑minute lunch, and five 10‑minute breaks) are incorporated to allocate contacts across time slots.

Two versions of the contact network are examined: a static network that aggregates all contacts over a single day, and a dynamic network that updates contacts at each time slot. Both are fed into an agent‑based influenza transmission model that simulates the spread of infection under three intervention scenarios: (i) no intervention, (ii) targeted antiviral prophylaxis (TAP) of high‑risk individuals, and (iii) grade‑level closure. The transmission probability per 10‑minute contact (p) is varied across a realistic range.

Simulation results reveal that the static network reproduces the epidemic curves produced by the dynamic network almost identically, indicating that a single‑day aggregated network captures the essential transmission pathways in this school setting. When comparing the network‑based model to a conventional random‑mixing model (where students mix uniformly within grades and classrooms), notable discrepancies emerge. For low transmission probabilities (p < 0.004 per 10 min), random mixing overestimates the effectiveness of TAP, suggesting that policy makers might be overly optimistic about targeted antiviral strategies under low‑transmissibility conditions. Conversely, for higher p (p > 0.004), random mixing underestimates TAP effectiveness. A similar threshold effect is observed for the final epidemic size, with the crossover around p ≈ 0.005. Grade‑closure interventions exhibit the same pattern: random mixing over‑predicts the benefit at low p and under‑predicts it at higher p.

The authors conclude that (1) a dyad‑independent ERGM is sufficient to represent the friendship structure relevant for disease spread, (2) contact behavior can be adequately captured by a static network derived from survey data, and (3) reliance on random‑mixing assumptions can lead to systematic bias in evaluating intervention strategies, especially near realistic transmission thresholds. The methodological pipeline—friendship ERGM → degree estimation → static contact network → transmission simulation—offers a cost‑effective yet data‑driven approach for schools and other institutions to assess influenza (or similar respiratory pathogen) dynamics and to design evidence‑based control policies.