High-resolution measurements of face-to-face contact patterns in a primary school

Abstract

Background: Little quantitative information is available on the mixing patterns of children in school environments. Describing and understanding contacts between children at school would help quantify the transmission opportunities of respiratory infections and identify situations within schools where the risk of transmission is higher. We report on measurements carried out in a French school (6-12 years children), where we collected data on the time-resolved face-to-face proximity of children and teachers using a proximity-sensing infrastructure based on radio frequency identification devices.

Methods and findings: Data on face-to-face interactions were collected on Thursday, October 1(st) and Friday, October 2(nd) 2009. We recorded 77,602 contact events between 242 individuals (232 children and 10 teachers). In this setting, each child has on average 323 contacts per day with 47 other children, leading to an average daily interaction time of 176 minutes. Most contacts are brief, but long contacts are also observed. Contacts occur mostly within each class, and each child spends on average three times more time in contact with classmates than with children of other classes. We describe the temporal evolution of the contact network and the trajectories followed by the children in the school, which constrain the contact patterns. We determine an exposure matrix aimed at informing mathematical models. This matrix exhibits a class and age structure which is very different from the homogeneous mixing hypothesis.

Conclusions: We report on important properties of the contact patterns between school children that are relevant for modeling the propagation of diseases and for evaluating control measures. We discuss public health implications related to the management of schools in case of epidemics and pandemics. Our results can help define a prioritization of control measures based on preventive measures, case isolation, classes and school closures, that could reduce the disruption to education during epidemics.

Figure 1. Total cumulated duration (A, in hours) and number of contacts (B) involving individuals of each class, for each day.

Figure 2. Boxplots of the distributions of the cumulated duration (A, in minutes) and number (B) of contacts involving an individual, for each class and for each day.

Panel C gives the distributions of the number of distinct individuals with whom an individual of each class has had at least one contact. In each boxplot, the horizontal line gives the median, the box extremities are the 25^th and 75^th percentiles, and the whiskers correspond to the 5^th and 95^th percentiles.

Figure 3. Log-log plot of the distribution of the contact durations and of the cumulated duration of all the contacts two individuals i and j have over a day (

). 88% of the contacts last less than 1 minute, but more than 0.2% last more than 5 minutes. For the cumulated durations, 64% of the total duration of contacts between two individuals during one day last less than 2 minutes, but 9% last more than 10 minutes and 0.38% more than 1 hour. The small symbols correspond to the original distributions, and the large symbols to the log-binned distributions.

Figure 4. Grayscale-coded contact matrix between classes.

The matrix entry for row A and column B gives the number of contacts () measured between individuals of classes A and B over the two days of data collection. A logarithmic grayscale is used to compress the dynamic range of the matrix entries and enhance the off-diagonal hierarchical structure.

Figure 5. Grayscale-coded contact matrix between classes.

The matrix entry for row A and column B gives the cumulated duration (, in minutes) of contacts measured between individuals of classes A and B over the two days of data gathering. A logarithmic grayscale is used to compress the dynamic range of the matrix entries and enhance the off-diagonal hierarchical structure.

Figure 6. Degree of individuals in the contact networks aggregated over sliding time windows of 20 minutes during the first day (left) and the second day (right) of data collection.

The median value is represented with a black line, the 95% confidence interval is shown in gray and the number of individuals over which the statistics are calculated is shown in red dashes. Breaks and beginning and end of lunch are characterized by a sudden increase of the degree, showing the occurrence of large numbers of contact events.

Figure 7. Time evolution of the average number of distinct children with whom a child has been in contact during the study.

The average total number is displayed in black, the average number of children of the same class in red, and the average number of children of other classes in blue.

Figure 8. Time evolution of the average cumulated time spent by a child in contact with other children during the study.

The average total time is displayed in black, the average time spent with children of the same class in red, and the average time spent with children of other classes in blue.

Figure 9. Network of contacts aggregated over the first day.

Edges between individuals having interacted less than 2 minutes have been removed, thus keeping only the strongest links. The width of links corresponds to the cumulative duration of contacts, and nodes with higher number of edges have larger size. Colors correspond to classes, teachers are shown in grey. Figure created using the Gephi software, http://www.gephi.org.

Figure 10. Approximate spatiotemporal trajectories of some classes.

Each row corresponds to a particular place in the school (classroom, canteen, courtyard) where a RFID reader was situated, and each colored line corresponds to the spatio-temporal trajectory of the children of a class (only 5 classes are shown for clarity). Line widths correspond to the number of children whose approximate position correspond to the row area. A line can become thinner if children leave the school (for instance during the lunch break, to have lunch at home) or divide itself into two thinner lines if two groups of children of the same class follow distinct paths in the school The trajectories highlight how mixing between classes, shown by the fact that the colored lines overlap, occurs during the breaks and is strongly constrained by the school schedule.