Information dynamics shape the sexual networks of Internet-mediated prostitution

Network Spreading from Network Dimension

Continuous-state network spreading models provide critical numerical and analytic insights into transmission processes in epidemiology, rumor propagation, knowledge dissemination, and many other areas. Most of these models reflect only local features such as adjacency, degree, and transitivity, so can exhibit substantial error in the presence of global correlations typical of empirical networks. Here, we propose mitigating this limitation via a network property ideally suited to capturing spreading. This is the network correlation dimension, which characterizes how the number of nodes within range of a source typically scales with distance. Applying the approach to susceptible-infected-recovered processes leads to a spreading model which, for a wide range of networks and epidemic parameters, can provide more accurate predictions of the early stages of a spreading process than important established models of substantially higher complexity. In addition, the proposed model leads to a basic reproduction number that provides information about the final state not available from popular established models.

Epidemic spreading under game-based self-quarantine behaviors: The different effects of local and global information

During the outbreak of an epidemic, individuals may modify their behaviors in response to external (including local and global) infection-related information. However, the difference between local and global information in influencing the spread of diseases remains inadequately explored. Here, we study a simple epidemic model that incorporates the game-based self-quarantine behavior of individuals, taking into account the influence of local infection status, global disease prevalence, and node heterogeneity (non-identical degree distribution). Our findings reveal that local information can effectively contain an epidemic, even with only a small proportion of individuals opting for self-quarantine. On the other hand, global information can cause infection evolution curves shaking during the declining phase of an epidemic, owing to the synchronous release of nodes with the same degree from the quarantined state. In contrast, the releasing pattern under the local information appears to be more random. This shaking phenomenon can be observed in various types of networks associated with different characteristics. Moreover, it is found that under the proposed game-epidemic framework, a disease is more difficult to spread in heterogeneous networks than in homogeneous networks, which differs from conventional epidemic models.

Statistical mechanics of inference in epidemic spreading

We investigate the information-theoretical limits of inference tasks in epidemic spreading on graphs in the thermodynamic limit. The typical inference tasks consist in computing observables of the posterior distribution of the epidemic model given observations taken from a ground-truth (sometimes called planted) random trajectory. We can identify two main sources of quenched disorder: the graph ensemble and the planted trajectory. The epidemic dynamics however induces nontrivial long-range correlations among individuals' states on the latter. This results in nonlocal correlated quenched disorder which unfortunately is typically hard to handle. To overcome this difficulty, we divide the dynamical process into two sets of variables: a set of stochastic independent variables (representing transmission delays), plus a set of correlated variables (the infection times) that depend deterministically on the first. Treating the former as quenched variables and the latter as dynamic ones, computing disorder average becomes feasible by means of the replica-symmetric cavity method. We give theoretical predictions on the posterior probability distribution of the trajectory of each individual, conditioned to observations on the state of individuals at given times, focusing on the susceptible infectious (SI) model. In the Bayes-optimal condition, i.e., when true dynamic parameters are known, the inference task is expected to fall in the replica-symmetric regime. We indeed provide predictions for the information theoretic limits of various inference tasks, in form of phase diagrams. We also identify a region, in the Bayes-optimal setting, with strong hints of replica-symmetry breaking. When true parameters are unknown, we show how a maximum-likelihood procedure is able to recover them with mostly unaffected performance.

Active querying approach to epidemic source detection on contact networks

The problem of identifying the source of an epidemic (also called patient zero) given a network of contacts and a set of infected individuals has attracted interest from a broad range of research communities. The successful and timely identification of the source can prevent a lot of harm as the number of possible infection routes can be narrowed down and potentially infected individuals can be isolated. Previous research on this topic often assumes that it is possible to observe the state of a substantial fraction of individuals in the network before attempting to identify the source. We, on the contrary, assume that observing the state of individuals in the network is costly or difficult and, hence, only the state of one or few individuals is initially observed. Moreover, we presume that not only the source is unknown, but also the duration for which the epidemic has evolved. From this more general problem setting a need to query the state of other (so far unobserved) individuals arises. In analogy with active learning, this leads us to formulate the active querying problem. In the active querying problem, we alternate between a source inference step and a querying step. For the source inference step, we rely on existing work but take a Bayesian perspective by putting a prior on the duration of the epidemic. In the querying step, we aim to query the states of individuals that provide the most information about the source of the epidemic, and to this end, we propose strategies inspired by the active learning literature. Our results are strongly in favor of a querying strategy that selects individuals for whom the disagreement between individual predictions, made by all possible sources separately, and a consensus prediction is maximal. Our approach is flexible and, in particular, can be applied to static as well as temporal networks. To demonstrate our approach's practical importance, we experiment with three empirical (temporal) contact networks: a network of pig movements, a network of sexual contacts, and a network of face-to-face contacts between residents of a village in Malawi. The results show that active querying strategies can lead to substantially improved source inference results as compared to baseline heuristics. In fact, querying only a small fraction of nodes in a network is often enough to achieve a source inference performance comparable to a situation where the infection states of all nodes are known.

Disrupting drive-by download networks on Twitter

This paper tests disruption strategies in Twitter networks containing malicious URLs used in drive-by download attacks. Cybercriminals use popular events that attract a large number of Twitter users to infect and propagate malware by using trending hashtags and creating misleading tweets to lure users to malicious webpages. Due to Twitter’s 280 character restriction and automatic shortening of URLs, it is particularly susceptible to the propagation of malware involved in drive-by download attacks. Considering the number of online users and the network formed by retweeting a tweet, a cybercriminal can infect millions of users in a short period. Policymakers and researchers have struggled to develop an efficient network disruption strategy to stop malware propagation effectively. We define an efficient strategy as one that considers network topology and dependency on network resilience, where resilience is the ability of the network to continue to disseminate information even when users are removed from it. One of the challenges faced while curbing malware propagation on online social platforms is understanding the cybercriminal network spreading the malware. Combining computational modelling and social network analysis, we identify the most effective strategy for disrupting networks of malicious URLs. Our results emphasise the importance of specific network disruption parameters such as network and emotion features, which have proved to be more effective in disrupting malicious networks compared to random strategies. In conclusion, disruption strategies force cybercriminal networks to become more vulnerable by strategically removing malicious users, which causes successful network disruption to become a long-term effort.

Exploring sexual contact networks by analyzing a nationwide commercial-sex review website

Understanding the structure of human sexual contact networks is vital in a broad range of disciplines, including sociology, biology, public health, and anthropology. However, sexual contact networks are yet to be understood because technical and privacy issues make it difficult to conduct accurate, large-scale surveys. In this study, we surveyed data openly available on one of the largest adult entertainment websites in Japan, where male clients (MCs) can write online customer reviews of female commercial sex workers (FCSWs). In particular, our investigation focused on a type of establishment called "soapland," the only type of sex industry in Japan where sexual intercourse is publicly permitted. Soaplands are scattered throughout Japan, and the study website covers approximately 66% of them. Using such a vast amount of data on a nationwide scale, we clarified the network structure of commercial sex, characterized by small-world, scale-free, and disassortative mating properties. To study geographical characteristics, we compared the resulting network with three different artificially generated networks via the random rewiring of links. Moreover, we considered a simple epidemic model on the resulting network, and investigated whether it would be more effective to provide infection control measures to FCSWs or MCs. We determined that active FCSWs constitute an important pathway of infection propagation in commercial sex networks, but MCs also play an essential role as weak ties.

Social diffusion sources can escape detection

Influencing others through social networks is fundamental to all human societies. Whether this happens through the diffusion of rumors, opinions, or viruses, identifying the diffusion source (i.e., the person that initiated it) is a problem that has attracted much research interest. Nevertheless, existing literature has ignored the possibility that the source might strategically modify the network structure (by rewiring links or introducing fake nodes) to escape detection. Here, without restricting our analysis to any particular diffusion scenario, we close this gap by evaluating two mechanisms that hide the source-one stemming from the source's actions, the other from the network structure itself. This reveals that sources can easily escape detection, and that removing links is far more effective than introducing fake nodes. Thus, efforts should focus on exposing concealed ties rather than planted entities; such exposure would drastically improve our chances of detecting the diffusion source.

Selling sex: what determines rates and popularity? An analysis of 11,500 online profiles

Sex work, or the exchange of sexual services for money or goods, is ubiquitous across eras and cultures. However, the practice of selling sex is often hidden due to stigma and the varying legal status of sex work. Online platforms that sex workers use to advertise services have become an increasingly important means of studying a market that is largely hidden. Although prior literature has primarily shed light on sex work from a public health or policy perspective (focusing largely on female sex workers), there are few studies that empirically research patterns of service provision in online sex work. This study investigated the determinants of pricing and popularity in the market for commercial sexual services online by using data from the largest UK network of online sexual services, a platform that is the industry-standard for sex workers. While the size of these influences varies across genders, nationality, age and the services provided are shown to be primary drivers of rates and popularity in sex work.

Non-selective distribution of infectious disease prevention may outperform risk-based targeting

Epidemic control often requires optimal distribution of available vaccines and prophylactic tools, to protect from infection those susceptible. Well-established theory recommends prioritizing those at the highest risk of exposure. But the risk is hard to estimate, especially for diseases involving stigma and marginalization. We address this conundrum by proving that one should target those at high risk only if the infection-averting efficacy of prevention is above a critical value, which we derive analytically. We apply this to the distribution of pre-exposure prophylaxis (PrEP) of the Human Immunodeficiency Virus (HIV) among men-having-sex-with-men (MSM), a population particularly vulnerable to HIV. PrEP is effective in averting infections, but its global scale-up has been slow, showing the need to revisit distribution strategies, currently risk-based. Using data from MSM communities in 58 countries, we find that non-selective PrEP distribution often outperforms risk-based, showing that a logistically simpler strategy is also more effective. Our theory may help design more feasible and successful prevention.

Pre-exposure prophylaxis (PrEP) is an effective HIV prevention measure but identifying those most at risk to target for treatment is challenging. Here, the authors demonstrate that non-selective PrEP distribution outperforms targeted strategies when use is not consistent, and/or prevalence of untreated HIV is high.

The global migration network of sex-workers

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.

Characterising the structure of the largest online commercial sex network in the UK: observational study with implications for STI prevention

This study analyses large-scale online data to examine the characteristics of a national commercial sex network of off-street female sex workers and their male clients to identify implications for public health policy and practice. We collected sexual contact information from the largest online community dedicated to reviewing sex workers' services in the UK. We built the sexual network using reviews reported between January 2014 and December 2017. We then quantified network parameters using social network analysis measures. The network is composed of 6477 vertices with 59% of them concentred in a giant component clustered around London and Milton Keynes. We found minimal disassortative mixing by degree between sex workers and their clients, and that a few clients and sex workers are highly connected whilst the majority only have one or few sexual contacts. Finally, our simulation models suggested that prevention strategies targeting both sex workers and clients with high centrality scores are the most effective in reducing network connectedness and average closeness centrality scores, thus limiting the transmission of STIs.

Dynamic hidden-variable network models

Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time and many exhibit dynamics of node characteristics as well as of linking structure. Here we introduce and study natural temporal extensions of static hidden-variable network models with stochastic dynamics of hidden variables and links. The dynamics is controlled by two parameters: one that tunes the rate of change of hidden variables and another that tunes the rate at which node pairs reevaluate their connections given the current values of hidden variables. Snapshots of networks in the dynamic models are equivalent to networks generated by the static models only if the link reevaluation rate is sufficiently larger than the rate of hidden-variable dynamics or if an additional mechanism is added whereby links actively respond to changes in hidden variables. Otherwise, links are out of equilibrium with respect to hidden variables and network snapshots exhibit structural deviations from the static models. We examine the level of structural persistence in the considered models and quantify deviations from staticlike behavior. We explore temporal versions of popular static models with community structure, latent geometry, and degree heterogeneity. While we do not attempt to directly model real networks, we comment on interesting qualitative resemblances to real systems. In particular, we speculate that links in some real networks are out of equilibrium with respect to hidden variables, partially explaining the presence of long-ranged links in geometrically embedded systems and intergroup connectivity in modular systems. We also discuss possible extensions, generalizations, and applications of the introduced class of dynamic network models.

Construction, comparison and evolution of networks in life sciences and other disciplines

Network approaches have become pervasive in many research fields. They allow for a more comprehensive understanding of complex relationships between entities as well as their group-level properties and dynamics. Many networks change over time, be it within seconds or millions of years, depending on the nature of the network. Our focus will be on comparative network analyses in life sciences, where deciphering temporal network changes is a core interest of molecular, ecological, neuropsychological and evolutionary biologists. Further, we will take a journey through different disciplines, such as social sciences, finance and computational gastronomy, to present commonalities and differences in how networks change and can be analysed. Finally, we envision how borrowing ideas from these disciplines could enrich the future of life science research.

Network reconstruction from infection cascades

Accessing the network through which a propagation dynamics diffuses is essential for understanding and controlling it. In a few cases, such information is available through direct experiments or thanks to the very nature of propagation data. In a majority of cases however, available information about the network is indirect and comes from partial observations of the dynamics, rendering the network reconstruction a fundamental inverse problem. Here we show that it is possible to reconstruct the whole structure of an interaction network and to simultaneously infer the complete time course of activation spreading, relying just on single epoch (i.e. snapshot) or time-scattered observations of a small number of activity cascades. The method that we present is built on a belief propagation approximation, that has shown impressive accuracy in a wide variety of relevant cases, and is able to infer interactions in the presence of incomplete time-series data by providing a detailed modelling of the posterior distribution of trajectories conditioned to the observations. Furthermore, we show by experiments that the information content of full cascades is relatively smaller than that of sparse observations or single snapshots.

Sex counts: An examination of sexual service advertisements in a UK online directory

Internationally, sex work research, public opinion, policy, laws, and practice are predicated on the assumption that commercial sex is a priori sold by women and bought by men. Scarce attention has been devoted to lesbian, gay, bisexual, transgender, or queer/questioning (LGBTQ) sex working as well as women who pay for sex. This is as much an empirical absence as it is a theoretical one, for the ideological claim that women comprise the "vast majority" of sex workers is rarely, if ever, exposed to empirical scrutiny. Focusing on the UK, we address this major gap in evidence in order to challenge the gendered and heterosexist logics that underpin contemporary debates. We do so by presenting large-scale data gained from the quantitative analysis of 25,511 registered member profiles of an online escort directory. Our findings point to heterogeneity rather than homogeneity in the contemporary sex industry including in terms of gender identity, sexual orientation, and advertised client base. For example, while two-thirds of advertisements self-identify as "Female," one in four are listed as "Male;" less than half list their sexual orientation as "Straight;" and nearly two-thirds advertise to women clients. Our study thus challenges prevailing heteronormative assumptions about commercial sex, which erase LGBTQ sex workers and other non-normative identities and practices, and which we argue have important political, practical, and theoretical consequences.

Long-tailed distributions of inter-event times as mixtures of exponential distributions

Inter-event times of various human behaviour are apparently non-Poissonian and obey long-tailed distributions as opposed to exponential distributions, which correspond to Poisson processes. It has been suggested that human individuals may switch between different states, in each of which they are regarded to generate events obeying a Poisson process. If this is the case, inter-event times should approximately obey a mixture of exponential distributions with different parameter values. In the present study, we introduce the minimum description length principle to compare mixtures of exponential distributions with different numbers of components (i.e. constituent exponential distributions). Because these distributions violate the identifiability property, one is mathematically not allowed to apply the Akaike or Bayes information criteria to their maximum-likelihood estimator to carry out model selection. We overcome this theoretical barrier by applying a minimum description principle to joint likelihoods of the data and latent variables. We show that mixtures of exponential distributions with a few components are selected, as opposed to more complex mixtures in various datasets, and that the fitting accuracy is comparable to that of state-of-the-art algorithms to fit power-law distributions to data. Our results lend support to Poissonian explanations of apparently non-Poissonian human behaviour.

Locating the Epidemic Source in Complex Networks with Sparse Observers

Epidemic source localization is one of the most meaningful areas of research in complex networks, which helps solve the problem of infectious disease spread. Limited by incomplete information of nodes and inevitable randomness of the spread process, locating the epidemic source becomes a little difficult. In this paper, we propose an efficient algorithm via Bayesian Estimation to locate the epidemic source and find the initial time in complex networks with sparse observers. By modeling the infected time of observers, we put forward a valid epidemic source localization method for tree network and further extend it to the general network via maximum spanning tree. The numerical analyses in synthetic networks and empirical networks show that our algorithm has a higher source localization accuracy than other comparison algorithms. In particular, when the randomness of the spread path enhances, our algorithm has a better performance. We believe that our method can provide an effective reference for epidemic spread and source localization in complex networks.

Contact-Based Model for Epidemic Spreading on Temporal Networks

We present a contact-based model to study the spreading of epidemics by means of extending the dynamic message-passing approach to temporal networks. The shift in perspective from node- to edge-centric quantities enables accurate modeling of Markovian susceptible-infected-recovered outbreaks on time-varying trees, i.e., temporal networks with a loop-free underlying topology. On arbitrary graphs, the proposed contact-based model incorporates potential structural and temporal heterogeneities of the contact network and improves analytic estimations with respect to the individual-based (node-centric) approach at a low computational and conceptual cost. Within this new framework, we derive an analytical expression for the epidemic threshold on temporal networks and demonstrate the feasibility of this method on empirical data.

The spread of infection, information, computer malware, or any contagionlike process is often described by disease models on complex networks with a time-varying topology. Recurrent, or flulike, spreading can be modeled accurately by taking an “individual-based” approach that focuses on nodes in a network. Here, we instead focus on the interactions—the links in a network—and present a contact-based model that accurately describes a second group of contagion processes: those that lead to permanent immunization. Taking this new perspective, we derive a criterion that separates local outbreaks from global epidemics, a crucial tool for risk assessment and control of, for instance, viral marketing.

To develop our model, we integrate time-varying network topologies into dynamic message passing, a widely used approach to describe unidirectional contagion processes. Based on this generalized model, we derive a spectral criterion for the stability of the disease-free solution, which determines the critical disease parameters. Through numerous numerical studies, we provide evidence that the contact-based perspective improves the individual-based approach. Finally, we investigate the epidemic risk based on the German cattle-trade network with over 180 000 nodes. Results from the individual-based and contact-based approaches deviate considerably, and thus justify this paradigmatic shift.

Our contact-based model is conceptually similar to those that focus on individuals, so we expect that numerous individual-based findings as well as results from networks with a static topology can be transferred in the future. These may include general epidemic models with a non-Poissonian transition process that go beyond the assumption of treelike topologies, stochastic effects, and temporal networks that evolve continuously in time.

NET-EXPO: A Gephi Plugin Towards Social Network Analysis of Network Exposure for Unipartite and Bipartite Graphs

Social network analysis (SNA) concerns itself in studying network structures in relation to individuals' behavior. Individuals may be influenced by their network members in their behavior, and thus past researchers have developed computational methods that allow us to measure the extent to which individuals are exposed to members with certain behavior within one's social network, and that be correlated with their own behavior. Some of these methods include network exposure model, affiliation exposure model, and decomposed network exposure models. We developed a Gephi plugin that computes and visualizes these various kinds of network exposure models called NET-EXPO. We experimented with NET-EXPO on some social network datasets to demonstrate its pragmatic use in social network research. This plugin has the potential to equip researchers with a tool to compute network exposures in a user friendly way and simplify the process to compute and visualize the network data.

Host contact dynamics shapes richness and dominance of pathogen strains

The interaction among multiple microbial strains affects the spread of infectious diseases and the efficacy of interventions. Genomic tools have made it increasingly easy to observe pathogenic strains diversity, but the best interpretation of such diversity has remained difficult because of relationships with host and environmental factors. Here, we focus on host-to-host contact behavior and study how it changes populations of pathogens in a minimal model of multi-strain interaction. We simulated a population of identical strains competing by mutual exclusion and spreading on a dynamical network of hosts according to a stochastic susceptible-infectious-susceptible model. We computed ecological indicators of diversity and dominance in strain populations for a collection of networks illustrating various properties found in real-world examples. Heterogeneities in the number of contacts among hosts were found to reduce diversity and increase dominance by making the repartition of strains among infected hosts more uneven, while strong community structure among hosts increased strain diversity. We found that the introduction of strains associated with hosts entering and leaving the system led to the highest pathogenic richness at intermediate turnover levels. These results were finally illustrated using the spread of Staphylococcus aureus in a long-term health-care facility where close proximity interactions and strain carriage were collected simultaneously. We found that network structural and temporal properties could account for a large part of the variability observed in strain diversity. These results show how stochasticity and network structure affect the population ecology of pathogens and warn against interpreting observations as unambiguous evidence of epidemiological differences between strains.

Conceptualizing Geosexual Archetypes: Mapping the Sexual Travels and Egocentric Sexual Networks of Gay and Bisexual Men in Toronto, Canada

Six geosexual archetypes were identified: hosters, house-callers, rovers, privates, travellers, and geoflexibles, each with different characteristic profiles. Prioritizing interventions to hosters, rovers, and geoflexibles may reduce sexually transmitted infection transmission.

Supplemental digital content is available in the text.

Background

There are complex, synergistic, and persistent sexually transmitted infection (STI) epidemics affecting gay, bisexual and other men who have sex with men (gbMSM) in every major urban centre across North America. We explored the spatial architecture of egocentric sexual networks for gbMSM in Toronto, Canada.

Methods

Our integrative mixed methods study included in-depth interviews with 31 gbMSM between May and July 2016. During interviews, participants mapped their egocentric sexual network for the preceding 3 months geographically. At the end, a self-administered survey was used to collect sociodemographic characteristics, online technology use, and STI testing and history.

Results

We identified 6 geosexual archetypes: hosters, house-callers, privates, rovers, travellers, and geoflexibles. Hosters always, or almost always (≥80%), hosted sex at their home. House-callers always, or almost always (≥80%), had sex at their partner’s home. Rovers always or almost always (≥80%) had sex at public venues (eg, bath houses, sex clubs) and other public spaces (eg, parks, cruising sites). Privates had sex in private—their own home or their partner's (part hoster, part house-caller). Travellers had sex away from their home, either at a partner’s home or some other venue or public space (part house-caller, part rover). Geoflexibles had sex in a variety of locations—their home, their partner’s home, or public venues. All hosters and rovers, and to a lesser extent, geoflexibles, reported a history of syphilis and human immunodeficiency virus.

Conclusions

Prioritizing interventions to hosters, rovers, and geoflexibles may have an important impact on reducing STI transmission.

Social network plasticity decreases disease transmission in a eusocial insect

Animal social networks are shaped by multiple selection pressures, including the need to ensure efficient communication and functioning while simultaneously limiting disease transmission. Social animals could potentially further reduce epidemic risk by altering their social networks in the presence of pathogens, yet there is currently no evidence for such pathogen-triggered responses. We tested this hypothesis experimentally in the ant Lasius niger using a combination of automated tracking, controlled pathogen exposure, transmission quantification, and temporally explicit simulations. Pathogen exposure induced behavioral changes in both exposed ants and their nestmates, which helped contain the disease by reinforcing key transmission-inhibitory properties of the colony's contact network. This suggests that social network plasticity in response to pathogens is an effective strategy for mitigating the effects of disease in social groups.

Identifying influential spreaders in complex networks by propagation probability dynamics

Numerous well-known processes of complex systems such as spreading and cascading are mainly affected by a small number of critical nodes. Identifying influential nodes that lead to broad spreading in complex networks is of great theoretical and practical importance. Since the identification of vital nodes is closely related to propagation dynamics, a novel method DynamicRank that employs the probability model to measure the ranking scores of nodes is suggested. The influence of a node can be denoted by the sum of probability scores of its i order neighboring nodes. This simple yet effective method provides a new idea to understand the identification of vital nodes in propagation dynamics. Experimental studies on both Susceptible-Infected-Recovered and Susceptible-Infected-Susceptible models in real networks demonstrate that it outperforms existing methods such as Coreness, H-index, LocalRank, Betweenness, and Spreading Probability in terms of the Kendall τ coefficient. The linear time complexity enables it to be applied to real large-scale networks with tens of thousands of nodes and edges in a short time.

Objective measures for sentinel surveillance in network epidemiology

Assume one has the capability of determining whether a node in a network is infectious or not by probing it. Then problem of optimizing sentinel surveillance in networks is to identify the nodes to probe such that an emerging disease outbreak can be discovered early or reliably. Whether the emphasis should be on early or reliable detection depends on the scenario in question. We investigate three objective measures from the literature quantifying the performance of nodes in sentinel surveillance: the time to detection or extinction, the time to detection, and the frequency of detection. As a basis for the comparison, we use the susceptible-infectious-recovered model on static and temporal networks of human contacts. We show that, for some regions of parameter space, the three objective measures can rank the nodes very differently. This means sentinel surveillance is a class of problems, and solutions need to chose an objective measure for the particular scenario in question. As opposed to other problems in network epidemiology, we draw similar conclusions from the static and temporal networks. Furthermore, we do not find one type of network structure that predicts the objective measures, i.e., that depends both on the data set and the SIR parameter values.

Disease persistence on temporal contact networks accounting for heterogeneous infectious periods

The infectious period of a transmissible disease is a key factor for disease spread and persistence. Epidemic models on networks typically assume an identical average infectious period for all individuals, thus allowing an analytical treatment. This simplifying assumption is, however, often unrealistic, as hosts may have different infectious periods, due, for instance, to individual host-pathogen interactions or inhomogeneous access to treatment. While previous work accounted for this heterogeneity in static networks, a full theoretical understanding of the interplay of varying infectious periods and time-evolving contacts is still missing. Here, we consider a susceptible-infectious-susceptible epidemic on a temporal network with host-specific average infectious periods, and develop an analytical framework to estimate the epidemic threshold, i.e. the critical transmissibility for disease spread in the host population. Integrating contact data for transmission with outbreak data and epidemiological estimates, we apply our framework to three real-world case studies exploring different epidemic contexts-the persistence of bovine tuberculosis in southern Italy, the spread of nosocomial infections in a hospital, and the diffusion of pandemic influenza in a school. We find that the homogeneous parametrization may cause important biases in the assessment of the epidemic risk of the host population. Our approach is also able to identify groups of hosts mostly responsible for disease diffusion who may be targeted for prevention and control, aiding public health interventions.

Graphlet-orbit Transitions (GoT): A fingerprint for temporal network comparison

Given a set of temporal networks, from different domains and with different sizes, how can we compare them? Can we identify evolutionary patterns that are both (i) characteristic and (ii) meaningful? We address these challenges by introducing a novel temporal and topological network fingerprint named Graphlet-orbit Transitions (GoT). We demonstrate that GoT provides very rich and interpretable network characterizations. Our work puts forward an extension of graphlets and uses the notion of orbits to encapsulate the roles of nodes in each subgraph. We build a transition matrix that keeps track of the temporal trajectory of nodes in terms of their orbits, therefore describing their evolution. We also introduce a metric (OTA) to compare two networks when considering these matrices. Our experiments show that networks representing similar systems have characteristic orbit transitions. GoT correctly groups synthetic networks pertaining to well-known graph models more accurately than competing static and dynamic state-of-the-art approaches by over 30%. Furthermore, our tests on real-world networks show that GoT produces highly interpretable results, which we use to provide insight into characteristic orbit transitions.

Dynamic topologies of activity-driven temporal networks with memory

We propose dynamic scaling in temporal networks with heterogeneous activities and memory and provide a comprehensive picture for the dynamic topologies of such networks, in terms of the modified activity-driven network model [H. Kim et al., Eur. Phys. J. B 88, 315 (2015)EPJBFY1434-602810.1140/epjb/e2015-60662-7]. Particularly, we focus on the interplay of the time resolution and memory in dynamic topologies. Through the random-walk (RW) process, we investigate diffusion properties and topological changes as the time resolution increases. Our results with memory are compared to those of the memoryless case. Based on the temporal percolation concept, we derive scaling exponents in the dynamics of the largest cluster and the coverage of the RW process in time-varying networks. We find that the time resolution in the time-accumulated network determines the effective size of the network, while memory affects relevant scaling properties at the crossover from the dynamic regime to the static one. The origin of memory-dependent scaling behaviors is the dynamics of the largest cluster, which depends on temporal degree distributions. Finally, we conjecture of the extended finite-size scaling ansatz for dynamic topologies and the fundamental property of temporal networks, which are numerically confirmed.

The fundamental advantages of temporal networks

Most networked systems of scientific interest are characterized by temporal links, meaning the network's structure changes over time. Link temporality has been shown to hinder many dynamical processes, from information spreading to accessibility, by disrupting network paths. Considering the ubiquity of temporal networks in nature, we ask: Are there any advantages of the networks' temporality? We use an analytical framework to show that temporal networks can, compared to their static counterparts, reach controllability faster, demand orders of magnitude less control energy, and have control trajectories, that are considerably more compact than those characterizing static networks. Thus, temporality ensures a degree of flexibility that would be unattainable in static networks, enhancing our ability to control them.

Sampling of temporal networks: Methods and biases

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.

Cost-efficient vaccination protocols for network epidemiology

We investigate methods to vaccinate contact networks—i.e. removing nodes in such a way that disease spreading is hindered as much as possible—with respect to their cost-efficiency. Any real implementation of such protocols would come with costs related both to the vaccination itself, and gathering of information about the network. Disregarding this, we argue, would lead to erroneous evaluation of vaccination protocols. We use the susceptible-infected-recovered model—the generic model for diseases making patients immune upon recovery—as our disease-spreading scenario, and analyze outbreaks on both empirical and model networks. For different relative costs, different protocols dominate. For high vaccination costs and low costs of gathering information, the so-called acquaintance vaccination is the most cost efficient. For other parameter values, protocols designed for query-efficient identification of the network’s largest degrees are most efficient.

Finding methods to identify important spreaders—and consequently protocols to identify individuals to vaccinate in targeted vaccination campaigns—is one of the most important topics of network theory. Earlier studies typically make some assumption about what information is available about the contact network that the disease spreads over. Then they try to optimize an objective function—either the average outbreak size in disease simulations, or (simpler) the size of the largest connected component. For public-health practitioners, gathering the network information cannot be detached from the decision process—their cost function includes the costs for both the vaccination itself and mapping of the network. This is the first paper to evaluate the cost efficiency of vaccination protocols—a problem that is much more relevant and not so much more complicated, than the oversimplified objective functions optimized in previous studies. We find a “no-free lunch” situation, where different protocols proposed in the past are most efficient at different cost scenarios. However, some methods are never cost efficient due to the amount of information they need. What protocol that is the best depends on network structure in a non-trivial way. We use both analytical and simulation techniques to reach these conclusions.

Optimizing sentinel surveillance in temporal network epidemiology

To help health policy makers gain response time to mitigate infectious disease threats, it is essential to have an efficient epidemic surveillance. One common method of disease surveillance is to carefully select nodes (sentinels, or sensors) in the network to report outbreaks. One would like to choose sentinels so that they discover the outbreak as early as possible. The optimal choice of sentinels depends on the network structure. Studies have addressed this problem for static networks, but this is a first step study to explore designing surveillance systems for early detection on temporal networks. This paper is based on the idea that vaccination strategies can serve as a method to identify sentinels. The vaccination problem is a related question that is much more  well studied for temporal networks. To assess the ability to detect epidemic outbreaks early, we calculate the time difference (lead time) between the surveillance set and whole population in reaching 1% prevalence. We find that the optimal selection of sentinels depends on both the network's temporal structures and the infection probability of the disease. We find that, for a mild infectious disease (low infection probability) on a temporal network in relation to potential disease spreading (the Prostitution network), the strategy of selecting latest contacts of random individuals provide the most amount of lead time. And for a more uniform, synthetic network with community structure the strategy of selecting frequent contacts of random individuals provide the most amount of lead time.

Inferring HIV-1 Transmission Dynamics in Germany From Recently Transmitted Viruses

BACKGROUND

Although HIV continues to spread globally, novel intervention strategies such as treatment as prevention (TasP) may bring the epidemic to a halt. However, their effective implementation requires a profound understanding of the underlying transmission dynamics.

METHODS

We analyzed parameters of the German HIV epidemic based on phylogenetic clustering of viral sequences from recently infected seroconverters with known infection dates. Viral baseline and follow-up pol sequences (n = 1943) from 1159 drug-naïve individuals were selected from a nationwide long-term observational study initiated in 1997. Putative transmission clusters were computed based on a maximum likelihood phylogeny. Using individual follow-up sequences, we optimized our clustering threshold to maximize the likelihood of co-clustering individuals connected by direct transmission.

RESULTS

The sizes of putative transmission clusters scaled inversely with their abundance and their distribution exhibited a heavy tail. Clusters based on the optimal clustering threshold were significantly more likely to contain members of the same or bordering German federal states. Interinfection times between co-clustered individuals were significantly shorter (26 weeks; interquartile range: 13-83) than in a null model.

CONCLUSIONS

Viral intraindividual evolution may be used to select criteria that maximize co-clustering of transmission pairs in the absence of strong adaptive selection pressure. Interinfection times of co-clustered individuals may then be an indicator of the typical time to onward transmission. Our analysis suggests that onward transmission may have occurred early after infection, when individuals are typically unaware of their serological status. The latter argues that TasP should be combined with HIV testing campaigns to reduce the possibility of transmission before TasP initiation.

From static to temporal network theory: Applications to functional brain connectivity

Network neuroscience has become an established paradigm to tackle questions related to the functional and structural connectome of the brain. Recently, interest has been growing in examining the temporal dynamics of the brain's network activity. Although different approaches to capturing fluctuations in brain connectivity have been proposed, there have been few attempts to quantify these fluctuations using temporal network theory. This theory is an extension of network theory that has been successfully applied to the modeling of dynamic processes in economics, social sciences, and engineering article but it has not been adopted to a great extent within network neuroscience. The objective of this article is twofold: (i) to present a detailed description of the central tenets of temporal network theory and describe its measures, and; (ii) to apply these measures to a resting-state fMRI dataset to illustrate their utility. Furthermore, we discuss the interpretation of temporal network theory in the context of the dynamic functional brain connectome. All the temporal network measures and plotting functions described in this article are freely available as the Python package Teneto.

Predicting epidemic evolution on contact networks from partial observations

The massive employment of computational models in network epidemiology calls for the development of improved inference methods for epidemic forecast. For simple compartment models, such as the Susceptible-Infected-Recovered model, Belief Propagation was proved to be a reliable and efficient method to identify the origin of an observed epidemics. Here we show that the same method can be applied to predict the future evolution of an epidemic outbreak from partial observations at the early stage of the dynamics. The results obtained using Belief Propagation are compared with Monte Carlo direct sampling in the case of SIR model on random (regular and power-law) graphs for different observation methods and on an example of real-world contact network. Belief Propagation gives in general a better prediction that direct sampling, although the quality of the prediction depends on the quantity under study (e.g. marginals of individual states, epidemic size, extinction-time distribution) and on the actual number of observed nodes that are infected before the observation time.

Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation

The dynamic of social networks is driven by the interplay between diverse mechanisms that still challenge our theoretical and modelling efforts. Amongst them, two are known to play a central role in shaping the networks evolution, namely the heterogeneous propensity of individuals to i) be socially active and ii) establish a new social relationships with their alters. Here, we empirically characterise these two mechanisms in seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the individuals’ social activity and their strategy in choosing ties where to allocate their social interactions can be quantitatively described and encoded in a simple stochastic network modelling framework. The Master Equation of the model can be solved in the asymptotic limit. The analytical solutions provide an explicit description of both the system dynamic and the dynamical scaling laws characterising crucial aspects about the evolution of the networks. The analytical predictions match with accuracy the empirical observations, thus validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other processes shaping social dynamics and to generate data driven predictions for the asymptotic behaviour of social networks.

Temporal network structures controlling disease spreading

We investigate disease spreading on eight empirical data sets of human contacts (mostly proximity networks recording who is close to whom, at what time). We compare three levels of representations of these data sets: temporal networks, static networks, and a fully connected topology. We notice that the difference between the static and fully connected networks-with respect to time to extinction and average outbreak size-is smaller than between the temporal and static topologies. This suggests that, for these data sets, temporal structures influence disease spreading more than static-network structures. To explain the details in the differences between the representations, we use 32 network measures. This study concurs that long-time temporal structures, like the turnover of nodes and links, are the most important for the spreading dynamics.

Inference of causality in epidemics on temporal contact networks

Investigating into the past history of an epidemic outbreak is a paramount problem in epidemiology. Based on observations about the state of individuals, on the knowledge of the network of contacts and on a mathematical model for the epidemic process, the problem consists in describing some features of the posterior distribution of unobserved past events, such as the source, potential transmissions, and undetected positive cases. Several methods have been proposed for the study of these inference problems on discrete-time, synchronous epidemic models on networks, including naive Bayes, centrality measures, accelerated Monte-Carlo approaches and Belief Propagation. However, most traced real networks consist of short-time contacts on continuous time. A possibility that has been adopted is to discretize time line into identical intervals, a method that becomes more and more precise as the length of the intervals vanishes. Unfortunately, the computational time of the inference methods increase with the number of intervals, turning a sufficiently precise inference procedure often impractical. We show here an extension of the Belief Propagation method that is able to deal with a model of continuous-time events, without resorting to time discretization. We also investigate the effect of time discretization on the quality of the inference.

Predicting the epidemic threshold of the susceptible-infected-recovered model

Researchers have developed several theoretical methods for predicting epidemic thresholds, including the mean-field like (MFL) method, the quenched mean-field (QMF) method, and the dynamical message passing (DMP) method. When these methods are applied to predict epidemic threshold they often produce differing results and their relative levels of accuracy are still unknown. We systematically analyze these two issues-relationships among differing results and levels of accuracy-by studying the susceptible-infected-recovered (SIR) model on uncorrelated configuration networks and a group of 56 real-world networks. In uncorrelated configuration networks the MFL and DMP methods yield identical predictions that are larger and more accurate than the prediction generated by the QMF method. As for the 56 real-world networks, the epidemic threshold obtained by the DMP method is more likely to reach the accurate epidemic threshold because it incorporates full network topology information and some dynamical correlations. We find that in most of the networks with positive degree-degree correlations, an eigenvector localized on the high k-core nodes, or a high level of clustering, the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input information, performs better than the other two methods.

Infections on Temporal Networks--A Matrix-Based Approach

We extend the concept of accessibility in temporal networks to model infections with a finite infectious period such as the susceptible-infected-recovered (SIR) model. This approach is entirely based on elementary matrix operations and unifies the disease and network dynamics within one algebraic framework. We demonstrate the potential of this formalism for three examples of networks with high temporal resolution: networks of social contacts, sexual contacts, and livestock-trade. Our investigations provide a new methodological framework that can be used, for instance, to estimate the epidemic threshold, a quantity that determines disease parameters, for which a large-scale outbreak can be expected.

Temporal and structural heterogeneities emerging in adaptive temporal networks

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.

Information content of contact-pattern representations and predictability of epidemic outbreaks

To understand the contact patterns of a population--who is in contact with whom, and when the contacts happen--is crucial for modeling outbreaks of infectious disease. Traditional theoretical epidemiology assumes that any individual can meet any with equal probability. A more modern approach, network epidemiology, assumes people are connected into a static network over which the disease spreads. Newer yet, temporal network epidemiology, includes the time in the contact representations. In this paper, we investigate the effect of these successive inclusions of more information. Using empirical proximity data, we study both outbreak sizes from unknown sources, and from known states of ongoing outbreaks. In the first case, there are large differences going from a fully mixed simulation to a network, and from a network to a temporal network. In the second case, differences are smaller. We interpret these observations in terms of the temporal network structure of the data sets. For example, a fast overturn of nodes and links seem to make the temporal information more important.

Finding Influential Spreaders from Human Activity beyond Network Location

Most centralities proposed for identifying influential spreaders on social networks to either spread a message or to stop an epidemic require the full topological information of the network on which spreading occurs. In practice, however, collecting all connections between agents in social networks can be hardly achieved. As a result, such metrics could be difficult to apply to real social networks. Consequently, a new approach for identifying influential people without the explicit network information is demanded in order to provide an efficient immunization or spreading strategy, in a practical sense. In this study, we seek a possible way for finding influential spreaders by using the social mechanisms of how social connections are formed in real networks. We find that a reliable immunization scheme can be achieved by asking people how they interact with each other. From these surveys we find that the probabilistic tendency to connect to a hub has the strongest predictive power for influential spreaders among tested social mechanisms. Our observation also suggests that people who connect different communities is more likely to be an influential spreader when a network has a strong modular structure. Our finding implies that not only the effect of network location but also the behavior of individuals is important to design optimal immunization or spreading schemes.

Complex dynamics of synergistic coinfections on realistically clustered networks

We investigate the impact of contact structure clustering on the dynamics of multiple diseases interacting through coinfection of a single individual, two problems typically studied independently. We highlight how clustering, which is well known to hinder propagation of diseases, can actually speed up epidemic propagation in the context of synergistic coinfections if the strength of the coupling matches that of the clustering. We also show that such dynamics lead to a first-order transition in endemic states, where small changes in transmissibility of the diseases can lead to explosive outbreaks and regions where these explosive outbreaks can only happen on clustered networks. We develop a mean-field model of coinfection of two diseases following susceptible-infectious-susceptible dynamics, which is allowed to interact on a general class of modular networks. We also introduce a criterion based on tertiary infections that yields precise analytical estimates of when clustering will lead to faster propagation than nonclustered networks. Our results carry importance for epidemiology, mathematical modeling, and the propagation of interacting phenomena in general. We make a call for more detailed epidemiological data of interacting coinfections.

Diffusion on networked systems is a question of time or structure

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.

Modes of interaction between individuals dominate the topologies of real world networks

We find that the topologies of real world networks, such as those formed within human societies, by the Internet, or among cellular proteins, are dominated by the mode of the interactions considered among the individuals. Specifically, a major dichotomy in previously studied networks arises from modeling networks in terms of pairwise versus group tasks. The former often intrinsically give rise to scale-free, disassortative, hierarchical networks, whereas the latter often give rise to single- or broad-scale, assortative, nonhierarchical networks. These dependencies explain contrasting observations among previous topological analyses of real world complex systems. We also observe this trend in systems with natural hierarchies, in which alternate representations of the same networks, but which capture different levels of the hierarchy, manifest these signature topological differences. For example, in both the Internet and cellular proteomes, networks of lower-level system components (routers within domains or proteins within biological processes) are assortative and nonhierarchical, whereas networks of upper-level system components (internet domains or biological processes) are disassortative and hierarchical. Our results demonstrate that network topologies of complex systems must be interpreted in light of their hierarchical natures and interaction types.

The basic reproduction number as a predictor for epidemic outbreaks in temporal networks

The basic reproduction number R₀—the number of individuals directly infected by an infectious person in an otherwise susceptible population—is arguably the most widely used estimator of how severe an epidemic outbreak can be. This severity can be more directly measured as the fraction of people infected once the outbreak is over, Ω. In traditional mathematical epidemiology and common formulations of static network epidemiology, there is a deterministic relationship between R₀ and Ω. However, if one considers disease spreading on a temporal contact network—where one knows when contacts happen, not only between whom—then larger R₀ does not necessarily imply larger Ω. In this paper, we numerically investigate the relationship between R₀ and Ω for a set of empirical temporal networks of human contacts. Among 31 explanatory descriptors of temporal network structure, we identify those that make R₀ an imperfect predictor of Ω. We find that descriptors related to both temporal and topological aspects affect the relationship between R₀ and Ω, but in different ways.

Predicting epidemic risk from past temporal contact data

Understanding how epidemics spread in a system is a crucial step to prevent and control outbreaks, with broad implications on the system’s functioning, health, and associated costs. This can be achieved by identifying the elements at higher risk of infection and implementing targeted surveillance and control measures. One important ingredient to consider is the pattern of disease-transmission contacts among the elements, however lack of data or delays in providing updated records may hinder its use, especially for time-varying patterns. Here we explore to what extent it is possible to use past temporal data of a system’s pattern of contacts to predict the risk of infection of its elements during an emerging outbreak, in absence of updated data. We focus on two real-world temporal systems; a livestock displacements trade network among animal holdings, and a network of sexual encounters in high-end prostitution. We define the node’s loyalty as a local measure of its tendency to maintain contacts with the same elements over time, and uncover important non-trivial correlations with the node’s epidemic risk. We show that a risk assessment analysis incorporating this knowledge and based on past structural and temporal pattern properties provides accurate predictions for both systems. Its generalizability is tested by introducing a theoretical model for generating synthetic temporal networks. High accuracy of our predictions is recovered across different settings, while the amount of possible predictions is system-specific. The proposed method can provide crucial information for the setup of targeted intervention strategies.

Following the emergence of a transmissible disease epidemic, interventions and resources need to be prioritized to efficiently control its spread. While the knowledge of the pattern of disease-transmission contacts among hosts would be ideal for this task, the continuously changing nature of such pattern makes its use less practical in real public health emergencies (or otherwise highly resource-demanding when possible). We show that in such situations critical knowledge to assess the real-time risk of infection can be extracted from past temporal contact data. An index expressing the conservation of contacts over time is proposed as an effective tool to prioritize interventions, and its efficiency is tested considering real data on livestock movements and on human sexual encounters.