Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion formation or the adoption of novelties, where complex mechanisms of influence and reinforcement are at work. Here we introduce a higher-order model of social contagion in which a social system is represented by a simplicial complex and contagion can occur through interactions in groups of different sizes. Numerical simulations of the model on both empirical and synthetic simplicial complexes highlight the emergence of novel phenomena such as a discontinuous transition induced by higher-order interactions. We show analytically that the transition is discontinuous and that a bistable region appears where healthy and endemic states co-exist. Our results help explain why critical masses are required to initiate social changes and contribute to the understanding of higher-order interactions in complex systems.

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. 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. 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.

Given their importance in shaping social networks and determining how information or transmissible diseases propagate in a population, interactions between individuals are the subject of many data collection efforts. To this aim, different methods are commonly used, ranging from diaries and surveys to decentralised infrastructures based on wearable sensors. These methods have each advantages and limitations but are rarely compared in a given setting. Moreover, as surveys targeting friendship relations might suffer less from memory biases than contact diaries, it is interesting to explore how actual contact patterns occurring in day-to-day life compare with friendship relations and with online social links. Here we make progresses in these directions by leveraging data collected in a French high school and concerning (i) face-to-face contacts measured by two concurrent methods, namely wearable sensors and contact diaries, (ii) self-reported friendship surveys, and (iii) online social links. We compare the resulting data sets and find that most short contacts are not reported in diaries while long contacts have a large reporting probability, and that the durations of contacts tend to be overestimated in the diaries. Moreover, measured contacts corresponding to reported friendship can have durations of any length but all long contacts do correspond to a reported friendship. On the contrary, online links that are not also reported in the friendship survey correspond to short face-to-face contacts, highlighting the difference of nature between reported friendships and online links. Diaries and surveys suffer moreover from a low sampling rate, as many students did not fill them, showing that the sensor-based platform had a higher acceptability. We also show that, despite the biases of diaries and surveys, the overall structure of the contact network, as quantified by the mixing patterns between classes, is correctly captured by both networks of self-reported contacts and of friendships, and we investigate the correlations between the number of neighbors of individuals in the three networks. Overall, diaries and surveys tend to yield a correct picture of the global structural organization of the contact network, albeit with much less links, and give access to a sort of backbone of the contact network corresponding to the strongest links, i.e., the contacts of longest cumulative durations.

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.

Face-to-face contacts between individuals contribute to shape social networks and play an important role in determining how infectious diseases can spread within a population. It is thus important to obtain accurate and reliable descriptions of human contact patterns occurring in various day-to-day life contexts. Recent technological advances and the development of wearable sensors able to sense proximity patterns have made it possible to gather data giving access to time-varying contact networks of individuals in specific environments. Here we present and analyze two such data sets describing with high temporal resolution the contact patterns of students in a high school. We define contact matrices describing the contact patterns between students of different classes and show the importance of the class structure. We take advantage of the fact that the two data sets were collected in the same setting during several days in two successive years to perform a longitudinal analysis on two very different timescales. We show the high stability of the contact patterns across days and across years: the statistical distributions of numbers and durations of contacts are the same in different periods, and we observe a very high similarity of the contact matrices measured in different days or different years. The rate of change of the contacts of each individual from one day to the next is also similar in different years. We discuss the interest of the present analysis and data sets for various fields, including in social sciences in order to better understand and model human behavior and interactions in different contexts, and in epidemiology in order to inform models describing the spread of infectious diseases and design targeted containment strategies.