Source-linked AI summary
Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers
Mathieu Génois, Christian L. Vestergaard, Julie Fournet, André Panisson, Isabelle Bonmarin, Alain Barrat
TL;DR
The paper asks how empirical office contact data can improve epidemic models and inform low-cost intervention strategies. It analyzes two weeks of sensor-recorded contacts, their network structure, and simulated SIR outbreaks. The sparse, department-structured network hinders rapidly spreading epidemics, while targeting cross-department linkers can efficiently prevent large outbreaks, subject to sampling and network-identification limitations.
Problem
Agent-based epidemic models need empirical interaction data to reduce arbitrariness, while the network structure of office contacts and its consequences for spreading require characterization.
Method
The authors analyze two weeks of wearable-sensor contact data, construct aggregated and temporal networks, simulate SIR epidemics, and classify nodes by their fraction of external departmental links.
Results
The sparse, department-structured network tends to hinder rapidly spreading epidemics, while linkers with approximately 50% external links act as bridges and are efficient vaccination targets.
Takeaways & Limitations
Linker behavior may be inferred from office organization or surveys, enabling efficient vaccination or social-distancing strategies with limited network information.
Takeaways & Limitations
Only part of the real contact network was observed, so the study assumes the sampled population represents the whole because sampling was high and departmentally uniform.
Abstract
from arXiv · showhide
Empirical data on contacts between individuals in social contexts play an important role in providing information for models describing human behavior and how epidemics spread in populations. Here, we analyze data on face-to-face contacts collected in an office building. The statistical properties of contacts are similar to other social situations, but important differences are observed in the contact network structure. In particular, the contact network is strongly shaped by the organization of the offices in departments, which has consequences in the design of accurate agent-based models of epidemic spread. We consider the contact network as a potential substrate for infectious disease spread and show that its sparsity tends to prevent outbreaks of rapidly spreading epidemics. Moreover, we define three typical behaviors according to the fraction $f$ of links each individual shares outside its own department: residents, wanderers and linkers. Linkers ($f\sim 50\%$) act as bridges in the network and have large betweenness centralities. Thus, a vaccination strategy targeting linkers efficiently prevents large outbreaks. As such a behavior may be spotted a priori in the offices' organization or from surveys, without the full knowledge of the time-resolved contact network, this result may help the design of efficient, low-cost vaccination or social-distancing strategies.
1 Introduction
The paper uses empirical face-to-face contact data to reduce arbitrariness in agent-based epidemic models. It examines how office organization shapes contact networks and evaluates vaccination based on individuals’ cross-department connections.
- 1 Introduction: Agent-based epidemic models require detailed interaction data, but their flexibility introduces arbitrariness in modeling choices.Empirical contact measurements can constrain assumptions about how individuals meet and how transmission occurs.
- 1 Introduction: Wearable sensors provide new data on human interactions, including the face-to-face contacts analyzed in this study.The data were collected using a SocioPatterns sensing infrastructure.
- 1 Introduction: The study examines how office departments determine contact-network structure and contact dynamics, and how these features affect epidemic spreading.It also evaluates vaccination strategies based on each person’s internal and external departmental links.
2 Data collection
The study collected anonymized face-to-face contact data from volunteers in one French office building over two weeks using wearable proximity sensors. Participation covered approximately two thirds of staff, with coverage varying across departments.
- 2 Data collection: Wearable chest-mounted sensors detected close proximity by exchanging ultra-low-power radio packets between participants.The body shields the radio frequencies used by the sensors, enabling detection of face-to-face proximity.
- 2 Data collection: The two-week study took place in an InVS office building near Paris containing three scientific departments, Human Resources, and Logistics.The departments were distributed across two office floors.
- 2 Data collection: Approximately two thirds of staff participated, with departmental coverage ranging from 63% to 87%.Participation required signed informed consent; data were anonymized and linked only to departments.
3.1 Aggregated and temporal contact networks
The authors construct aggregated and temporal contact networks from two weeks of sensor data and compare their contact statistics with conference and high-school datasets. Contact distributions are broadly similar across settings, while the office network is organized by departments.
- 3.1 Aggregated and temporal contact networks: The aggregated network links two individuals when they had at least one contact during the two-week study, with link weights equal to total contact duration.The time-resolved data additionally support contact-duration and inter-contact-time analyses.
- 3.1 Aggregated and temporal contact networks: The empirical network visualization represents individuals as nodes, departments by color, and observed contacts as links.Force Atlas layout makes network communities apparent.
- 3.1 Aggregated and temporal contact networks: The office contact data show broad, approximately power-law-shaped distributions of link weights, contact times, and inter-contact times, similar to conference and high-school data.The comparison covers normalized degrees, link weights, contact times, and inter-contact times.
3.2 Sparsity of the contacts and consequences for the potential spread of infectious diseases
The office contact network is sparse, creating few transmission opportunities and hindering large outbreaks at moderate spreading ratios. Temporal ordering further constrains fast epidemics, so increasing transmission and recovery rates can suppress large outbreaks at fixed β/µ.
- 3.2 Sparsity of the contacts and consequences for the potential spread of infectious diseases: 15 average contacts per individual represented only ∼15% of the participating office population over two weeks.This sparsity makes the network far from fully connected and affects infectious-disease propagation.
- 3.2 Sparsity of the contacts and consequences for the potential spread of infectious diseases: 1000 simulations per parameter value estimated final epidemic-size distributions from randomly chosen seeds and start times on repeated time-resolved contact sequences.The SIR model used infection rate β, recovery rate µ, and inactivity during nights and weekends.
- 3.2 Sparsity of the contacts and consequences for the potential spread of infectious diseases: For β/µ = 100, simulations produced no large outbreaks because sparse contacts made infection propagation difficult.At 20-second resolution, the average instantaneous degree was 0.013 and the whole network had 0.66 links on average.
- 3.2 Sparsity of the contacts and consequences for the potential spread of infectious diseases: For β/µ = 1000, many simulations still produced small epidemics, although some affected a large fraction of the population.Increasing β/µ can compensate for the low contact rate sufficiently to permit larger epidemics.
- 3.2 Sparsity of the contacts and consequences for the potential spread of infectious diseases: At fixed β/µ, faster spreading and recovery tend to suppress the large-epidemic mode because temporal ordering and inactivity constrain transmission pathways.A contact sequence can enable or prevent an individual from serving as an intermediary between successive contacts.
3.3 Organization in departments
The office contact network is strongly shaped by departmental organization rather than homogeneous mixing. Internal contacts dominate, while external contacts form structured connections among departments.
- The five departments occupy two floors, with three logistics/scientific departments and cafeteria facilities downstairs and human resources and DSE upstairs.
- Contacts occur much more often within departments than between them, except in logistics.
- External contacts do not simply follow the two-floor layout; scientific departments form a moderately connected sub-structure.
- Canteen contacts differ markedly, showing mostly diagonal mixing patterns with little interaction between departments.
- Although office schedules impose few strict constraints, departmental organization produces patterns far from homogeneous mixing, affecting epidemic-model design.
3.4 Weak inter-department ties
Internal links are stronger and more clustered than links between departments. Topological overlap and contact duration both distinguish these two types of ties.
- Topological overlap O_ij measures how similarly connected two linked individuals are through their shared neighbors.O_ij = n_ij/((k_i−1)+(k_j−1)−n_ij), with values from 0 for no shared neighbors to 1 for identical neighborhoods.
- Internal links have average overlap 0.29±? and average weight 328±? s, compared with 0.13±? and 134±? s for inter-department links.
- Overlap and link weight are positively correlated, indicating that longer contacts tend to connect individuals with more similar neighborhoods.
- Contact matrices quantify total contact time between departments across the building, conference room, cafeteria, and canteen.
3.5 Daily contacts structure
Department-level contact patterns remain stable across days, while the precise daily network fluctuates substantially. Aggregating over longer periods steadily increases observed connectivity and contact duration.
- Daily contact-matrix similarities remain high, including when diagonal elements are excluded, showing that primary and secondary structures persist across days.
- Mean degree increases steadily as the network is aggregated over longer intervals for both internal and external links.
- Daily network similarities exceed those of random rewiring, degree-preserving rewiring, weight redistribution, and department-preserving null models.
- The precise daily contact networks fluctuate significantly, but their day-to-day changes are smaller than expected by random chance.
- Total contact duration within and between departments also grows steadily during aggregation.
- Whole-building activity peaks around 10am and lunchtime, with no other clear global temporal feature.
4 Node behaviors
Individuals are classified by the fraction of links outside their department, revealing linkers as the most central bridge-like nodes. Vaccinating linkers substantially reduces large-outbreak risk with less information than exact centrality targeting.
- 4.1 Residents, wanderers and linkers: Linkers have approximately half internal and half external links and occupy the highest-centrality portion of the aggregated network.Residents and wanderers have low centralities, whereas linkers act as bridges between departments.
- 4.2 Linkers and spreading processes: Linker detection requires less information than identifying the nodes with the highest centrality, although it is less precise.
- 4.2 Linkers and spreading processes: Targeting linkers decreases both the probability and size of large outbreaks, outperforming random vaccination.
- 4.2 Linkers and spreading processes: At a vaccination rate of 20%, linker targeting performs almost as well as centrality-based vaccination while strongly reducing outbreak probability.
- 4.2 Linkers and spreading processes: At 5% vaccination, linker targeting does not greatly reduce outbreak probability but produces smaller epidemics when outbreaks occur than random vaccination.
- 4.3 Stability of the linker behavior: Linker behavior is fairly stable over time: most two-week linkers retain 40%–60% external links in one-week aggregates, and one week may suffice for identification.
5 Discussion
The sampled office contact network is structured by departments and contains residents, wanderers, and linker behaviors. Although identifying linkers precisely requires contact-network knowledge, their behavior may be inferred more cheaply from organizational information or surveys.
- Study scope: The analysis assumes the sampled population represents the whole office because participation was high and sampling was uniform across departments.Not all individuals participated, so the observed network covers only part of the real contact network.
- Network structure: Contacts are sparse and department structure differs from homogeneous mixing, tending to hinder rapidly spreading epidemics.Department connections reflect organizational roles: scientific departments cluster, while human resources and logistics are more isolated.
- Node behaviors: Residents have mostly internal links, wanderers mostly external links, and linkers split links between departments to bridge communities.The behaviors are defined by each node’s fraction of links within its own department.
- Practical constraints: Precise linker identification relies on knowledge of the contact network, creating an information requirement for the strategy.This requirement is comparable to identifying nodes with highest betweenness centrality.
- Practical constraints: Organizational charts, professional grade, or specific activities may reveal likely linkers and support lower-cost vaccination strategies.The proposed information can be available without complete time-resolved contact data.
7 Supplementary information
The supplementary analyses compare contact-matrix constructions, temporal representations, and null models, then evaluate how these choices affect simulated epidemic sizes. They show that static or homogeneous representations can overestimate large outbreaks when they fail to preserve contact sparsity and temporal structure.
- 7.1 Contact matrices: Contact matrices can be normalized by department size or possible links, changing interpretation from total contact time to mean contact duration.Row normalization yields the mean time each node from the row department spends in contact with the other department.
- 7.1 Contact matrices: Daily contact-matrix similarities remain large across normalization procedures, although their values depend on the chosen normalization.The comparison uses cosine similarities between daily matrices, with and without diagonals.
- 7.1 Contact matrices: A presence-timeline null model with random same-location encounters produces a contact matrix significantly different from the empirical matrix.Thus, empirical matrix structure is not explained by random encounters among individuals sharing presence timelines.
- 7.2 Effect of data representation on epidemic spreading.: For β/µ = 100, most simulated epidemics remain small across representations, but contact matrices and homogeneous mixing produce broader epidemic-size tails.These representations do not correctly preserve contact sparsity.
- 7.2 Effect of data representation on epidemic spreading.: For β/µ = 1000, time-resolved contacts suppress the large-epidemic mode for faster epidemics, whereas static representations strongly overestimate it.Shorter recovery times make temporal contact patterns more consequential for spread.
- 7.2 Effect of data representation on epidemic spreading.: The simulations support using representations that retain sufficient information about contact-network sparsity and heterogeneity.The conclusion is consistent with results obtained in another social context.
Face-to-face contacts in an office building 27
The supplementary epidemic analysis examines distributions of epidemic sizes under an SIR model across infection rates. It uses repeated simulations while fixing the recovering rate through a constant β/µ ratio.
- Epidemic-size simulations: The analysis studies distributions of epidemic size N for different infection rates β.The recovering rate µ is adjusted so that β/µ remains constant.
- Epidemic-size simulations: For each infection-rate value, the epidemic-size statistics are computed from 1000 simulations.The repeated simulations provide the distributions shown in the supplementary figure.
- Epidemic-size simulations: The supplementary figure compares epidemic-size distributions across infection-rate settings under a fixed β/µ ratio.The stated setup varies β while holding the ratio constant through µ.