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Human interactions create social networks forming the backbone of societies. Individuals adjust their opinions by exchanging information through social interactions. Two recurrent questions are whether social structures promote opinion polarisation or consensus and whether polarisation can be avoided, particularly on social media. In this paper, we hypothesise that not only network structure but also the timings of social interactions regulate the emergence of opinion clusters. We devise a temporal version of the Deffuant opinion model where pairwise social interactions follow temporal patterns. Individuals may self-organise into a multi-partisan society due to network clustering promoting the reinforcement of local opinions. Burstiness has a similar effect and is alone sufficient to refrain the population from consensus and polarisation by also promoting the reinforcement of local opinions. The diversity of opinions in socially clustered networks thus increases with burstiness, particularly, and counter-intuitively, when individuals have low tolerance and prefer to adjust to similar peers. The emergent opinion landscape is well-balanced regarding groups' size, with relatively short differences between groups, and a small fraction of extremists. We argue that polarisation is more likely to emerge in social media than offline social networks because of the relatively low social clustering observed online, despite the observed online burstiness being sufficient to promote more diversity than would be expected offline. Increasing the variance of burst activation times, e.g. by being less active on social media, could be a venue to reduce polarisation. Furthermore, strengthening online social networks by increasing social redundancy, i.e. triangles, may also promote diversity., (© 2024. The Author(s).)

Temporal (or time-evolving) networks are commonly used to model complex systems and the evolution of their components throughout time. Although these networks can be analyzed by different means, visual analytics stands out as an effective way for a pre-analysis before doing quantitative/statistical analyses to identify patterns, anomalies, and other behaviors in the data, thus leading to new insights and better decision-making. However, the large number of nodes, edges, and/or timestamps in many real-world networks may lead to polluted layouts that make the analysis inefficient or even infeasible. In this paper, we propose LargeNetVis, a web-based visual analytics system designed to assist in analyzing small and large temporal networks. It successfully achieves this goal by leveraging three taxonomies focused on network communities to guide the visual exploration process. The system is composed of four interactive visual components: the first (Taxonomy Matrix) presents a summary of the network characteristics, the second (Global View) gives an overview of the network evolution, the third (a node-link diagram) enables community- and node-level structural analysis, and the fourth (a Temporal Activity Map - TAM) shows the community- and node-level activity under a temporal perspective. We demonstrate the usefulness and effectiveness of LargeNetVis through two usage scenarios and a user study with 14 participants.

Background: Vaccines are promising tools to control the spread of COVID-19. An effective vaccination campaign requires government policies and community engagement, sharing experiences for social support, and voicing concerns about vaccine safety and efficiency. The increasing use of online social platforms allows us to trace large-scale communication and infer public opinion in real time., Objective: This study aimed to identify the main themes in COVID-19 vaccine-related discussions on Twitter in Japan and track how the popularity of the tweeted themes evolved during the vaccination campaign. Furthermore, we aimed to understand the impact of critical social events on the popularity of the themes., Methods: We collected more than 100 million vaccine-related tweets written in Japanese and posted by 8 million users (approximately 6.4% of the Japanese population) from January 1 to October 31, 2021. We used Latent Dirichlet Allocation to perform automated topic modeling of tweet text during the vaccination campaign. In addition, we performed an interrupted time series regression analysis to evaluate the impact of 4 critical social events on public opinion., Results: We identified 15 topics grouped into the following 4 themes: (1) personal issue, (2) breaking news, (3) politics, and (4) conspiracy and humor. The evolution of the popularity of themes revealed a shift in public opinion, with initial sharing of attention over personal issues (individual aspect), collecting information from news (knowledge acquisition), and government criticism to focusing on personal issues. Our analysis showed that the Tokyo Olympic Games affected public opinion more than other critical events but not the course of vaccination. Public opinion about politics was significantly affected by various social events, positively shifting attention in the early stages of the vaccination campaign and negatively shifting attention later., Conclusions: This study showed a striking shift in public interest in Japan, with users splitting their attention over various themes early in the vaccination campaign and then focusing only on personal issues, as trust in vaccines and policies increased. An interrupted time series regression analysis showed that the vaccination rollout to the general population (under 65 years) increased the popularity of tweets about practical advice and personal vaccination experience, and the Tokyo Olympic Games disrupted public opinion but not the course of the vaccination campaign. The methodology developed here allowed us to monitor the evolution of public opinion and evaluate the impact of social events on public opinion, using large-scale Twitter data., (©Ryota Kobayashi, Yuka Takedomi, Yuri Nakayama, Towa Suda, Takeaki Uno, Takako Hashimoto, Masashi Toyoda, Naoki Yoshinaga, Masaru Kitsuregawa, Luis E C Rocha. Originally published in the Journal of Medical Internet Research (https://www.jmir.org), 22.12.2022.)

Differences in the social and economic environment across countries encourage humans to migrate in search of better living conditions, including job opportunities, higher salaries, security and welfare. Quantifying global migration is, however, challenging because of poor recording, privacy issues and residence status. This is particularly critical for some classes of migrants involved in stigmatised, unregulated or illegal activities. Escorting services or high-end prostitution are well-paid activities that attract workers all around the world. In this paper, we study international migration patterns of sex-workers by using network methods. Using an extensive international online advertisement directory of escorting services and information about individual escorts, we reconstruct a migrant flow network where nodes represent either origin or destination countries. The links represent the direct routes between two countries. The migration network of sex-workers shows different structural patterns than the migration of the general population. The network contains a strong core where mutual migration is often observed between a group of high-income European countries, yet Europe is split into different network communities with specific ties to non-European countries. We find non-reciprocal relations between countries, with some of them mostly offering while others attract workers. The Gross Domestic Product per capita (GDPc) is a good indicator of country attractiveness for incoming workers and service rates but is unrelated to the probability of emigration. The median financial gain of migrating, in comparison to working at the home country, is 15.9 % . Only sex-workers coming from 77 % of the countries have financial gains with migration and average gains decrease with the GDPc of the country of origin. Our results suggest that high-end sex-worker migration is regulated by economic, geographic and cultural aspects., Competing Interests: Conflict of interestThe authors declare that they have no conflict of interest., (© The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2022.)

Recently proposed computational techniques allow the application of various maximum entropy network models at a larger scale. We focus on disinformation campaigns and apply different maximum entropy network models on the collection of datasets from the Twitter information operations report. For each dataset, we obtain additional Twitter data required to build an interaction network. We consider different interaction networks which we compare to an appropriate null model. The null model is used to identify statistically significant interactions. We validate our method and evaluate to what extent it is suited to identify communities of members of a disinformation campaign in a non-supervised way. We find that this method is suitable for larger social networks and allows to identify statistically significant interactions between users. Extracting the statistically significant interaction leads to the prevalence of users involved in a disinformation campaign being higher. We found that the use of different network models can provide different perceptions of the data and can lead to the identification of different meaningful patterns. We also test the robustness of the methods to illustrate the impact of missing data. Here we observe that sampling the correct data is of great importance to reconstruct an entire disinformation operation., Competing Interests: Competing interestsThe authors declare that they have no competing interests., (© The Author(s) 2022.)

Social animals self-organise to create groups to increase protection against predators and productivity. One-to-one interactions are the building blocks of these emergent social structures and may correspond to friendship, grooming, communication, among other social relations. These structures should be robust to failures and provide efficient communication to compensate the costs of forming and maintaining the social contacts but the specific purpose of each social interaction regulates the evolution of the respective social networks. We collate 611 animal social networks and show that the number of social contacts E scales with group size N as a super-linear power-law [Formula: see text] for various species of animals, including humans, other mammals and non-mammals. We identify that the power-law exponent [Formula: see text] varies according to the social function of the interactions as [Formula: see text], with [Formula: see text]. By fitting a multi-layer model to our data, we observe that the cost to cross social groups also varies according to social function. Relatively low costs are observed for physical contact, grooming and group membership which lead to small groups with high and constant social clustering. Offline friendship has similar patterns while online friendship shows weak social structures. The intermediate case of spatial proximity (with [Formula: see text] and clustering dependency on network size quantitatively similar to friendship) suggests that proximity interactions may be as relevant for the spread of infectious diseases as for social processes like friendship.

Background: HIV Pre-exposure prophylaxis (PrEP) is being considered for implementation among MSM nationwide in Vietnam. However, there may be concerns about potential obstacles for PrEP adherence among Vietnamese MSM. This study aims to assess the acceptability to use PrEP, potential barriers and facilitators, and the preferences for PrEP service accessibility and delivery among Vietnamese MSM., Methods: Four focus group discussions (FGDs) were conducted with 30 HIV-negative MSM in January 2018 in Hanoi, Vietnam. FGDs explored MSM's awareness regarding PrEP, perceived benefits and barriers of PrEP use, and willingness to use PrEP. FGDs were audio-recorded and transcribed verbatim. Content analysis was used., Results: The mean age of participants was 23.9 years old. Most participants realized the advantages of PrEP given its efficacy in HIV risk reduction and expressed high motivation and interest to use PrEP in the future. PrEP was considered as a supplement alongside condoms. Common concerns about PrEP included side-effects, forgetting to take the pill daily, stigmatization due to using PrEP, negative attitudes toward PrEP from other MSM and accessibility of PrEP. Participants would prefer an injectable PrEP regime if available as it was seen as easier to adhere to. Concerns were also raised that PrEP usage could be interpreted as an indication of engaging in sexual risk behavior for HIV, potentially causing suspicion in love relationships or by family and friends. Participants preferred to receive PrEP in civil business organizations and MSM-friendly clinics, and recommended that pharmacy stores would not be suitable for PrEP implementation due to lack of trust and fear of fake drugs., Conclusion: This study indicated a high level of willingness to use PrEP among MSM in Vietnam in combination with condom. Strategies to raise awareness of PrEP, reduce stigma towards PrEP, and improve the accessibility among MSM in Vietnam is needed. Existing MSM-friendly clinics were recommended to implement PrEP programs in Vietnam.

Background: Web-based respondent-driven sampling is a novel sampling method for the recruitment of participants for generating population estimates, studying social network characteristics, and delivering health interventions. However, the application, barriers and facilitators, and recruitment performance of web-based respondent-driven sampling have not yet been systematically investigated., Objective: Our objectives were to provide an overview of published research using web-based respondent-driven sampling and to investigate factors related to the recruitment performance of web-based respondent-driven sampling., Methods: We conducted a scoping review on web-based respondent-driven sampling studies published between 2000 and 2019. We used the process evaluation of complex interventions framework to gain insights into how web-based respondent-driven sampling was implemented, what mechanisms of impact drove recruitment, what the role of context was in the study, and how these components together influenced the recruitment performance of web-based respondent-driven sampling., Results: We included 18 studies from 8 countries (high- and low-middle income countries), in which web-based respondent-driven sampling was used for making population estimates (n=12), studying social network characteristics (n=3), and delivering health-related interventions (n=3). Studies used web-based respondent-driven sampling to recruit between 19 and 3448 participants from a variety of target populations. Studies differed greatly in the number of seeds recruited, the proportion of successfully recruiting participants, the number of recruitment waves, the type of incentives offered to participants, and the duration of data collection. Studies that recruited relatively more seeds, through online platforms, and with less rigorous selection procedures reported relatively low percentages of successfully recruiting seeds. Studies that did not offer at least one guaranteed material incentive reported relatively fewer waves and lower percentages of successfully recruiting participants. The time of data collection was shortest in studies with university students., Conclusions: Web-based respondent-driven sampling can be successfully applied to recruit individuals for making population estimates, studying social network characteristics, and delivering health interventions. In general, seed and peer recruitment may be enhanced by rigorously selecting and motivating seeds, offering at least one guaranteed material incentive, and facilitating adequate recruitment options regarding the target population's online connectedness and communication behavior. Potential trade-offs should be taken into account when implementing web-based respondent-driven sampling, such as having less opportunities to implement rigorous seed selection procedures when recruiting many seeds, as well as issues around online rather than physical participation, such as the risk of cheaters participating repeatedly., (©Yannick B Helms, Nora Hamdiui, Mirjam E E Kretzschmar, Luis E C Rocha, Jim E van Steenbergen, Linus Bengtsson, Anna Thorson, Aura Timen, Mart L Stein. Originally published in the Journal of Medical Internet Research (http://www.jmir.org), 15.01.2021.)

Games involving virtual worlds are popular in several segments of the population and societies. The online environment facilitates that players from different countries interact in a common virtual world. Virtual worlds involving social and economic interactions are particularly useful to test social and economic theories. Using data from EVE Online, a massive online multi-player game simulating a fantasy galaxy, we analyse the relation between the real-world context in which players live and their in-game behaviour at the country level. We find that in-game aggressiveness to non-player characters is positively related to real-world levels of aggressiveness as measured by the Global Peace Index and the Global Terrorist Index at the country level. The opposite is true for in-game aggressiveness towards other players, which seems to work as a safety valve for real-world player aggressiveness. The ability to make in-game friends is also positively related to real-world levels of aggressiveness in much the same way. In-game trading behaviour is dependent on the macro-economic environment where players live. The unemployment rate and exchange rate make players trade more efficiently and cautiously in-game. Overall, we find evidence that the real-world environment affects in-game behaviour, suggesting that virtual worlds can be used to experiment and test social and economic theories, and to infer real-world behaviour at the country level., Competing Interests: The authors have declared that no competing interests exist.

Background: Electronic health (eHealth) interventions are promising in HIV and sexually transmitted infections (STIs) prevention among men who have sex with men (MSM), given a high rate of the Internet use in this population. This study determined the preferences for eHealth interventions to prevent HIV and STIs among MSM in Hanoi, Vietnam to guide the development of future eHealth interventions., Methods: Five focus group discussions (FGD) were conducted with 35 MSM recruited by purposive sampling in January 2018 in Hanoi, Vietnam. The FGDs addressed attitudes towards the feasibility and uptake of HIV/STI interventions via online modalities such as smartphone applications (apps, social network sites, or emails); preferences and concerns regarding an online HIV/STI intervention. FGDs were audio-recorded and transcribed verbatim. Content analysis was used to determine themes., Results: MSM reported that they commonly searched for information regarding HIV/STI and sexual health on Facebook and a variety of mobile apps. They perceived a lack of reliable online sources, a high need, and interest for an online intervention. Most of them preferred short and concise messages without perceived sensitive words such as "HIV" or "STI". Diversity of online modalities were preferred with information from credible sources about HIV/STI symptoms, testing and treatment, safe sex practices and testing locations with a focus on safe MSM-friendly clinics. Concerns about the need to trust the organization behind the online information and interventions, and the importance of confidentiality when participating in online interventions were raised., Conclusion: High acceptance and perceived need for an online HIV/STI intervention were reported. The importance of establishing trust within the MSM community as a reliable source of information was emphasized, as well as the importance of confidentiality.

Methicillin-resistant Staphylococcus aureus (MRSA) is a difficult-to-treat infection. Increasing efforts have been taken to mitigate the epidemics and to avoid potential outbreaks in low endemic settings. Understanding the population dynamics of MRSA is essential to identify the causal mechanisms driving the epidemics and to generalise conclusions to different contexts. Previous studies neglected the temporal structure of contacts between patients and assumed homogeneous behaviour. We developed a high-resolution data-driven contact network model of interactions between 743,182 patients in 485 hospitals during 3,059 days to reproduce the exact contact sequences of the hospital population. Our model captures the exact spatial and temporal human contact behaviour and the dynamics of referrals within and between wards and hospitals at a large scale, revealing highly heterogeneous contact and mobility patterns of individual patients. A simulation exercise of epidemic spread shows that heterogeneous contacts cause the emergence of super-spreader patients, slower than exponential polynomial growth of the prevalence, and fast epidemic spread between wards and hospitals. In our simulated scenarios, screening upon hospital admittance is potentially more effective than reducing infection probability to reduce the final outbreak size. Our findings are useful to understand not only MRSA spread but also other hospital-acquired infections.

Background: Early detection, identification, and treatment of chronic hepatitis B through screening is vital for those at increased risk, e.g. born in hepatitis B endemic countries. In the Netherlands, Moroccan immigrants show low participation rates in health-related screening programmes. Since social networks influence health behaviour, we investigated whether similar screening intentions for chronic hepatitis B cluster within social networks of Moroccan immigrants., Methods: We used respondent-driven sampling (RDS) where each participant ("recruiter") was asked to complete a questionnaire and to recruit three Moroccans ("recruitees") from their social network. Logistic regression analyses were used to analyse whether the recruiters' intention to request a screening test was similar to the intention of their recruitees., Results: We sampled 354 recruiter-recruitee pairs: for 154 pairs both participants had a positive screening intention, for 68 pairs both had a negative screening intention, and the remaining 132 pairs had a discordant intention to request a screening test. A tie between a recruiter and recruitee was associated with having the same screening intention, after correction for sociodemographic variables (OR 1.70 [1.15-2.51])., Conclusions: The findings of our pilot study show clustering of screening intention among individuals in the same network. This provides opportunities for social network interventions to encourage participation in hepatitis B screening initiatives.

A systematic review was conducted to summarize and appraise the eHealth interventions addressing HIV/STI prevention among men who have sex with men (MSM), and characterize features of successful eHealth interventions. Fifty-five articles (17 pilots and 38 full efficacy trials) were included with the predominance of web-based interventions in the United States-based settings. Intervention modalities include web-based, short message service (SMS)/text messges/email reminder, online video-based, computer-assisted, multimedia-based, social network, live chat and chat room, virtual simulation intervention, and smartphone applications. Forty-nine eHealth interventions achieved a short-term behaviour change among participants. Four studies were conducted with 12-month follow-ups; and only one of them could maintain the behaviour change over this longer time period which could be due to the lack of booster interventions. Our study suggests that eHealth interventions can achieve short term behaviour change among MSM, however limited interventions could maintain behaviour change over 12 months. Further eHealth intervention strategies to promote HIV prevention among MSM should be conducted and rigorously evaluated.

Modern technology has drastically changed the way we interact and consume information. For example, online social platforms allow for seamless communication exchanges at an unprecedented scale. However, we are still bounded by cognitive and temporal constraints. Our attention is limited and extremely valuable. Algorithmic personalisation has become a standard approach to tackle the information overload problem. As result, the exposure to our friends' opinions and our perception about important issues might be distorted. However, the effects of algorithmic gatekeeping on our hyper-connected society are poorly understood. Here, we devise an opinion dynamics model where individuals are connected through a social network and adopt opinions as function of the view points they are exposed to. We apply various filtering algorithms that select the opinions shown to each user (i) at random (ii) considering time ordering or (iii) its current opinion. Furthermore, we investigate the interplay between such mechanisms and crucial features of real networks. We found that algorithmic filtering might influence opinions' share and distributions, especially in case information is biased towards the current opinion of each user. These effects are reinforced in networks featuring topological and spatial correlations where echo chambers and polarisation emerge. Conversely, heterogeneity in connectivity patterns reduces such tendency. We consider also a scenario where one opinion, through nudging, is centrally pushed to all users. Interestingly, even minimal nudging is able to change the status quo moving it towards the desired view point. Our findings suggest that simple filtering algorithms might be powerful tools to regulate opinion dynamics taking place on social networks.

Achievement gaps refer to the difference in the performance on assessments of students belonging to different social groups. Achievement gaps between ethnic groups have been observed in countries with heterogeneous populations. In this paper, achievement gaps between ethnic populations in Brazil were analyzed by studying the performance of a large cohort of senior high-school students in a standardized national exam. Ethnic groups were stratified by Brazilian states and socio-economic variables to homogeneize the groups, and the analyses focused on the disciplines of mathematics and writing that involve different cognitive functions. A Welch's t -test analysis was performed and key socio-economic variables that may explain the gaps were studied. The results show that gaps between ethnic groups of students living in low-income households were either statistically insignificant or small (2- 6 % ) if statistically significant. Larger gaps however were observed for students coming from high-income families in some contexts. Although parental education was associated with higher performance, it may either increase, decrease or maintain the gaps between White and Black, and between White and Pardo students. Our results support that socio-economic variables, linked to historical developments, have an impact on student's performance irrespective of ethnic background, resulting on little to no influence on group performance when students are exposed to similar cultural and economic contexts.

The Syrian armed conflict has been ongoing since 2011 and has already caused thousands of deaths. The analysis of death tolls helps to understand the dynamics of the conflict and to better allocate resources and aid to the affected areas. In this article, we use information on the daily number of deaths to study temporal and spatial correlations in the data, and exploit this information to forecast events of deaths. We found that the number of violent deaths per day in Syria varies more widely than that in England in which non-violent deaths dominate. We have identified strong positive auto-correlations in Syrian cities and non-trivial cross-correlations across some of them. The results indicate synchronization in the number of deaths at different times and locations, suggesting respectively that local attacks are followed by more attacks at subsequent days and that coordinated attacks may also take place across different locations. Thus the analysis of high temporal resolution data across multiple cities makes it possible to infer attack strategies, warn potential occurrence of future events, and hopefully avoid further deaths.

Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example, human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is that they are sampled within temporal and spatial frames. Furthermore, one might wish to subsample networks to reduce their size for better visualization or to perform computationally intensive simulations. The sampling method may affect the network structure and thus caution is necessary to generalize results based on samples. In this paper, we study four sampling strategies applied to a variety of real-life temporal networks. We quantify the biases generated by each sampling strategy on a number of relevant statistics such as link activity, temporal paths and epidemic spread. We find that some biases are common in a variety of networks and statistics, but one strategy, uniform sampling of nodes, shows improved performance in most scenarios. Given the particularities of temporal network data and the variety of network structures, we recommend that the choice of sampling methods be problem oriented to minimize the potential biases for the specific research questions on hand. Our results help researchers to better design network data collection protocols and to understand the limitations of sampled temporal network data.

The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We develop an individual-based approximation for the susceptible-infected-recovered epidemic model applicable to arbitrary dynamic networks. Our framework provides, at the individual-level, the probability flow over time associated with the infection dynamics. This computationally efficient framework discards the correlation between the states of different nodes, yet provides accurate results in approximating direct numerical simulations. It naturally captures the temporal heterogeneities and correlations of contact sequences, fundamental ingredients regulating the timing and size of an epidemic outbreak, and the number of secondary infections. The high accuracy of our approximation further allows us to detect the index individual of an epidemic outbreak in real-life network data.

We introduce a model of adaptive temporal networks whose evolution is regulated by an interplay between node activity and dynamic exchange of information through links. We study the model by using a master equation approach. Starting from a homogeneous initial configuration, we show that temporal and structural heterogeneities, characteristic of real-world networks, spontaneously emerge. This theoretically tractable model thus contributes to the understanding of the dynamics of human activity and interaction networks.

Urbanization promotes economy, mobility, access, and availability of resources, but on the other hand, generates higher levels of pollution, violence, crime, and mental distress. The health consequences of the agglomeration of people living close together are not fully understood. Particularly, it remains unclear how variations in the population size across cities impact the health of the population. We analyze the deviations from linearity of the scaling of several health-related quantities, such as the incidence and mortality of diseases, external causes of death, wellbeing, and health care availability, in respect to the population size of cities in Brazil, Sweden, and the USA. We find that deaths by non-communicable diseases tend to be relatively less common in larger cities, whereas the per capita incidence of infectious diseases is relatively larger for increasing population size. Healthier lifestyle and availability of medical support are disproportionally higher in larger cities. The results are connected with the optimization of human and physical resources and with the non-linear effects of social networks in larger populations. An urban advantage in terms of health is not evident, and using rates as indicators to compare cities with different population sizes may be insufficient.

Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the strong assumption that networks are static entities where temporal aspects can be neglected. Here we propose a generalized formalism for linear dynamics on complex networks, able to incorporate statistical properties of the timings at which events occur. We show that the diffusion dynamics is affected by the network community structure and by the temporal properties of waiting times between events. We identify the main mechanism--network structure, burstiness or fat tails of waiting times--determining the relaxation times of stochastic processes on temporal networks, in the absence of temporal-structure correlations. We identify situations when fine-scale structure can be discarded from the description of the dynamics or, conversely, when a fully detailed model is required due to temporal heterogeneities.

Networks are commonly used to define underlying interaction structures where infections, information, or other quantities may spread. Although the standard approach has been to aggregate all links into a static structure, some studies have shown that the time order in which the links are established may alter the dynamics of spreading. In this paper, we study the impact of the time ordering in the limits of flow on various empirical temporal networks. By using a random walk dynamics, we estimate the flow on links and convert the original undirected network (temporal and static) into a directed flow network. We then introduce the concept of flow motifs and quantify the divergence in the representativity of motifs when using the temporal and static frameworks. We find that the regularity of contacts and persistence of vertices (common in email communication and face-to-face interactions) result on little differences in the limits of flow for both frameworks. On the other hand, in the case of communication within a dating site and of a sexual network, the flow between vertices changes significantly in the temporal framework such that the static approximation poorly represents the structure of contacts. We have also observed that cliques with 3 and 4 vertices containing only low-flow links are more represented than the same cliques with all high-flow links. The representativity of these low-flow cliques is higher in the temporal framework. Our results suggest that the flow between vertices connected in cliques depend on the topological context in which they are placed and in the time sequence in which the links are established. The structure of the clique alone does not completely characterize the potential of flow between the vertices.

The dynamic nature of contact patterns creates diverse temporal structures. In particular, empirical studies have shown that contact patterns follow heterogeneous inter-event time intervals, meaning that periods of high activity are followed by long periods of inactivity. To investigate the impact of these heterogeneities in the spread of infection from a theoretical perspective, we propose a stochastic model to generate temporal networks where vertices make instantaneous contacts following heterogeneous inter-event intervals, and may leave and enter the system. We study how these properties affect the prevalence of an infection and estimate R(0), the number of secondary infections of an infectious individual in a completely susceptible population, by modeling simulated infections (SI and SIR) that co-evolve with the network structure. We find that heterogeneous contact patterns cause earlier and larger epidemics in the SIR model in comparison to homogeneous scenarios for a vast range of parameter values, while smaller epidemics may happen in some combinations of parameters. In the case of SI and heterogeneous patterns, the epidemics develop faster in the earlier stages followed by a slowdown in the asymptotic limit. For increasing vertex turnover rates, heterogeneous patterns generally cause higher prevalence in comparison to homogeneous scenarios with the same average inter-event interval. We find that [Formula: see text] is generally higher for heterogeneous patterns, except for sufficiently large infection duration and transmission probability.

Decreasing the number of people who must be vaccinated to immunize a community against an infectious disease could both save resources and decrease outbreak sizes. A key to reaching such a lower threshold of immunization is to find and vaccinate people who, through their behavior, are more likely than average to become infected and to spread the disease further. Fortunately, the very behavior that makes these people important to vaccinate can help us to localize them. Earlier studies have shown that one can use previous contacts to find people that are central in static contact networks. However, real contact patterns are not static. In this paper, we investigate if there is additional information in the temporal contact structure for vaccination protocols to exploit. We answer this affirmative by proposing two immunization methods that exploit temporal correlations and showing that these methods outperform a benchmark static-network protocol in four empirical contact datasets under various epidemic scenarios. Both methods rely only on obtainable, local information, and can be implemented in practice. For the datasets directly related to contact patterns of potential disease spreading (of sexually-transmitted and nosocomial infections respectively), the most efficient protocol is to sample people at random and vaccinate their latest contacts. The network datasets are temporal, which enables us to make more realistic evaluations than earlier studies--we use only information about the past for the purpose of vaccination, and about the future to simulate disease outbreaks. Using analytically tractable models, we identify two temporal structures that explain how the protocols earn their efficiency in the empirical data. This paper is a first step towards real vaccination protocols that exploit temporal-network structure--future work is needed both to characterize the structure of real contact sequences and to devise immunization methods that exploit these.

Sexual contact patterns, both in their temporal and network structure, can influence the spread of sexually transmitted infections (STI). Most previous literature has focused on effects of network topology; few studies have addressed the role of temporal structure. We simulate disease spread using SI and SIR models on an empirical temporal network of sexual contacts in high-end prostitution. We compare these results with several other approaches, including randomization of the data, classic mean-field approaches, and static network simulations. We observe that epidemic dynamics in this contact structure have well-defined, rather high epidemic thresholds. Temporal effects create a broad distribution of outbreak sizes, even if the per-contact transmission probability is taken to its hypothetical maximum of 100%. In general, we conclude that the temporal correlations of our network accelerate outbreaks, especially in the early phase of the epidemics, while the network topology (apart from the contact-rate distribution) slows them down. We find that the temporal correlations of sexual contacts can significantly change simulated outbreaks in a large empirical sexual network. Thus, temporal structures are needed alongside network topology to fully understand the spread of STIs. On a side note, our simulations further suggest that the specific type of commercial sex we investigate is not a reservoir of major importance for HIV.

Like many other social phenomena, prostitution is increasingly coordinated over the Internet. The online behavior affects the offline activity; the reverse is also true. We investigated the reported sexual contacts between 6,624 anonymous escorts and 10,106 sex buyers extracted from an online community from its beginning and six years on. These sexual encounters were also graded and categorized (in terms of the type of sexual activities performed) by the buyers. From the temporal, bipartite network of posts, we found a full feedback loop in which high grades on previous posts affect the future commercial success of the sex worker, and vice versa. We also found a peculiar growth pattern in which the turnover of community members and sex workers causes a sublinear preferential attachment. There is, moreover, a strong geographic influence on network structure--the network is geographically clustered but still close to connected, the contacts consistent with the inverse-square law observed in trading patterns. We also found that the number of sellers scales sublinearly with city size, so this type of prostitution does not, comparatively speaking, benefit much from an increasing concentration of people.