Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees.

BACKGROUND: The spread of infectious diseases crucially depends on the pattern of contacts between individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. However, there are few empirical studies available that provide estimates of the number and duration of contacts between social groups. Moreover, their space and time resolutions are limited, so that data are not explicit at the person-to-person level, and the dynamic nature of the contacts is disregarded. In this study, we aimed to assess the role of data-driven dynamic contact patterns between individuals, and in particular of their temporal aspects, in shaping the spread of a simulated epidemic in the population. METHODS: We considered high-resolution data about face-to-face interactions between the attendees at a conference, obtained from the deployment of an infrastructure based on radiofrequency identification (RFID) devices that assessed mutual face-to-face proximity. The spread of epidemics along these interactions was simulated using an SEIR (Susceptible, Exposed, Infectious, Recovered) model, using both the dynamic network of contacts defined by the collected data, and two aggregated versions of such networks, to assess the role of the data temporal aspects. RESULTS: We show that, on the timescales considered, an aggregated network taking into account the daily duration of contacts is a good approximation to the full resolution network, whereas a homogeneous representation that retains only the topology of the contact network fails to reproduce the size of the epidemic. CONCLUSIONS: These results have important implications for understanding the level of detail needed to correctly inform computational models for the study and management of real epidemics. Please see related article BMC Medicine, 2011, 9:88.

What's in a crowd? Analysis of face-to-face behavioral networks.

The availability of new data sources on human mobility is opening new avenues for investigating the interplay of social networks, human mobility and dynamical processes such as epidemic spreading. Here we analyze data on the time-resolved face-to-face proximity of individuals in large-scale real-world scenarios. We compare two settings with very different properties, a scientific conference and a long-running museum exhibition. We track the behavioral networks of face-to-face proximity, and characterize them from both a static and a dynamic point of view, exposing differences and similarities. We use our data to investigate the dynamics of a susceptible-infected model for epidemic spreading that unfolds on the dynamical networks of human proximity. The spreading patterns are markedly different for the conference and the museum case, and they are strongly impacted by the causal structure of the network data. A deeper study of the spreading paths shows that the mere knowledge of static aggregated networks would lead to erroneous conclusions about the transmission paths on the dynamical networks.

Social network dynamics of face-to-face interactions.

The recent availability of data describing social networks is changing our understanding of the "microscopic structure" of a social tie. A social tie indeed is an aggregated outcome of many social interactions such as face-to-face conversations or phone calls. Analysis of data on face-to-face interactions shows that such events, as many other human activities, are bursty, with very heterogeneous durations. In this paper we present a model for social interactions at short time scales, aimed at describing contexts such as conference venues in which individuals interact in small groups. We present a detailed analytical and numerical study of the model's dynamical properties, and show that it reproduces important features of empirical data. The model allows for many generalizations toward an increasingly realistic description of social interactions. In particular, in this paper we investigate the case where the agents have intrinsic heterogeneities in their social behavior, or where dynamic variations of the local number of individuals are included. Finally we propose this model as a very flexible framework to investigate how dynamical processes unfold in social networks.

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

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.

Dynamical and bursty interactions in social networks.

We present a modeling framework for dynamical and bursty contact networks made of agents in social interaction. We consider agents' behavior at short time scales in which the contact network is formed by disconnected cliques of different sizes. At each time a random agent can make a transition from being isolated to being part of a group or vice versa. Different distributions of contact times and intercontact times between individuals are obtained by considering transition probabilities with memory effects, i.e., the transition probabilities for each agent depend both on its state (isolated or interacting) and on the time elapsed since the last change in state. The model lends itself to analytical and numerical investigations. The modeling framework can be easily extended and paves the way for systematic investigations of dynamical processes occurring on rapidly evolving dynamical networks, such as the propagation of an information or spreading of diseases.