Indirect influence in social networks as an induced percolation phenomenon.

Percolation theory has been widely used to study phase transitions in network systems. It has also successfully explained various macroscopic spreading phenomena across different fields. Yet, the theoretical frameworks have been focusing on direct interactions among nodes, while recent empirical observations have shown that indirect interactions are common in many network systems like social and ecological networks, among others. By investigating the detailed mechanism of both direct and indirect influence on scientific collaboration networks, here we show that indirect influence can play the dominant role in behavioral influence. To address the lack of theoretical understanding of such indirect influence on the macroscopic behavior of the system, we propose a percolation mechanism of indirect interactions called induced percolation. Surprisingly, our model exhibits a unique anisotropy property. Specifically, directed networks show first-order abrupt transitions as opposed to the second-order continuous transition in the same network structure but with undirected links. A mix of directed and undirected links leads to rich hybrid phase transitions. Furthermore, a unique feature of the nonmonotonic pattern is observed in network connectivities near the critical point. We also present an analytical framework to characterize the proposed induced percolation, paving the way to further understanding network dynamics with indirect interactions.

Quantifying the importance and location of SARS-CoV-2 transmission events in large metropolitan areas.

Detailed characterization of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission across different settings can help design less disruptive interventions. We used real-time, privacy-enhanced mobility data in the New York City, NY and Seattle, WA metropolitan areas to build a detailed agent-based model of SARS-CoV-2 infection to estimate the where, when, and magnitude of transmission events during the pandemic's first wave. We estimate that only 18% of individuals produce most infections (80%), with about 10% of events that can be considered superspreading events (SSEs). Although mass gatherings present an important risk for SSEs, we estimate that the bulk of transmission occurred in smaller events in settings like workplaces, grocery stores, or food venues. The places most important for transmission change during the pandemic and are different across cities, signaling the large underlying behavioral component underneath them. Our modeling complements case studies and epidemiological data and indicates that real-time tracking of transmission events could help evaluate and define targeted mitigation policies.

Unraveling the COVID-19 hospitalization dynamics in Spain using Bayesian inference.

BACKGROUND: One of the main challenges of the COVID-19 pandemic is to make sense of available, but often heterogeneous and noisy data. This contribution presents a data-driven methodology that allows exploring the hospitalization dynamics of COVID-19, exemplified with a study of 17 autonomous regions in Spain from summer 2020 to summer 2021. METHODS: We use data on new daily cases and hospitalizations reported by the Spanish Ministry of Health to implement a Bayesian inference method that allows making short-term predictions of bed occupancy of COVID-19 patients in each of the autonomous regions of the country. RESULTS: We show how to use the temporal series for the number of daily admissions and discharges from hospital to reproduce the hospitalization dynamics of COVID-19 patients. For the case-study of the region of Aragon, we estimate that the probability of being admitted to hospital care upon infection is 0.090 [0.086-0.094], (95% C.I.), with the distribution governing hospital admission yielding a median interval of 3.5 days and an IQR of 7 days. Likewise, the distribution on the length of stay produces estimates of 12 days for the median and 10 days for the IQR. A comparison between model parameters for the regions analyzed allows to detect differences and changes in policies of the health authorities. CONCLUSIONS: We observe important regional differences, signaling that to properly compare very different populations, it is paramount to acknowledge all the diversity in terms of culture, socio-economic status, and resource availability. To better understand the impact of this pandemic, much more data, disaggregated and properly annotated, should be made available.

Deterrence through punishment can resolve collective risk dilemmas in carbon emission games.

Collective risk social dilemmas are at the heart of the most pressing global challenges we are facing today, including climate change mitigation and the overuse of natural resources. Previous research has framed this problem as a public goods game (PGG), where a dilemma arises between short-term interests and long-term sustainability. In the PGG, subjects are placed in groups and asked to choose between cooperation and defection, while keeping in mind their personal interests as well as the commons. Here, we explore how and to what extent the costly punishment of defectors is successful in enforcing cooperation by means of human experiments. We show that an apparent irrational underestimation of the risk of being punished plays an important role, and that for sufficiently high punishment fines, this vanishes and the threat of deterrence suffices to preserve the commons. Interestingly, however, we find that high fines not only avert freeriders, but they also demotivate some of the most generous altruists. As a consequence, the tragedy of the commons is predominantly averted due to cooperators that contribute only their "fair share" to the common pool. We also find that larger groups require larger fines for the deterrence of punishment to have the desired prosocial effect.

Robustness and Complexity of Directed and Weighted Metabolic Hypergraphs.

Metabolic networks are probably among the most challenging and important biological networks. Their study provides insight into how biological pathways work and how robust a specific organism is against an environment or therapy. Here, we propose a directed hypergraph with edge-dependent vertex weight as a novel framework to represent metabolic networks. This hypergraph-based representation captures higher-order interactions among metabolites and reactions, as well as the directionalities of reactions and stoichiometric weights, preserving all essential information. Within this framework, we propose the communicability and the search information as metrics to quantify the robustness and complexity of directed hypergraphs. We explore the implications of network directionality on these measures and illustrate a practical example by applying them to a small-scale E. coli core model. Additionally, we compare the robustness and the complexity of 30 different models of metabolism, connecting structural and biological properties. Our findings show that antibiotic resistance is associated with high structural robustness, while the complexity can distinguish between eukaryotic and prokaryotic organisms.

Impact of vaccine hesitancy on secondary COVID-19 outbreaks in the US: an age-structured SIR model.

BACKGROUND: The COVID-19 outbreak has become the worst pandemic in at least a century. To fight this disease, a global effort led to the development of several vaccines at an unprecedented rate. There have been, however, several logistic issues with its deployment, from their production and transport, to the hesitancy of the population to be vaccinated. For different reasons, an important amount of individuals is reluctant to get the vaccine, something that hinders our ability to control and-eventually-eradicate the disease. MATERIALS AND METHODS: Our aim is to explore the impact of vaccine hesitancy when highly transmissible SARS-CoV-2 variants of concern spread through a partially vaccinated population. To do so, we use age-stratified data from surveys on vaccination acceptance, together with age-contact matrices to inform an age-structured SIR model set in the US. RESULTS: Our results show that per every one percent decrease in vaccine hesitancy up to 45 deaths per million inhabitants could be averted. A closer inspection of the stratified infection rates also reveals the important role played by the youngest groups. The model captures the general trends of the Delta wave spreading in the US (July-October 2021) with a correlation coefficient of [Formula: see text]. CONCLUSIONS: Our results shed light on the role that hesitancy plays on COVID-19 mortality and highlight the importance of increasing vaccine uptake in the population, specially among the eldest age groups.

Multilayer networks with higher-order interaction reveal the impact of collective behavior on epidemic dynamics.

The ongoing COVID-19 pandemic has inflicted tremendous economic and societal losses. In the absence of pharmaceutical interventions, the population behavioral response, including situational awareness and adherence to non-pharmaceutical intervention policies, has a significant impact on contagion dynamics. Game-theoretic models have been used to reproduce the concurrent evolution of behavioral responses and disease contagion, and social networks are critical platforms on which behavior imitation between social contacts, even dispersed in distant communities, takes place. Such joint contagion dynamics has not been sufficiently explored, which poses a challenge for policies aimed at containing the infection. In this study, we present a multi-layer network model to study contagion dynamics and behavioral adaptation. It comprises two physical layers that mimic the two solitary communities, and one social layer that encapsulates the social influence of agents from these two communities. Moreover, we adopt high-order interactions in the form of simplicial complexes on the social influence layer to delineate the behavior imitation of individual agents. This model offers a novel platform to articulate the interaction between physically isolated communities and the ensuing coevolution of behavioral change and spreading dynamics. The analytical insights harnessed therefrom provide compelling guidelines on coordinated policy design to enhance the preparedness for future pandemics.

Data-driven contact structures: From homogeneous mixing to multilayer networks.

The modeling of the spreading of communicable diseases has experienced significant advances in the last two decades or so. This has been possible due to the proliferation of data and the development of new methods to gather, mine and analyze it. A key role has also been played by the latest advances in new disciplines like network science. Nonetheless, current models still lack a faithful representation of all possible heterogeneities and features that can be extracted from data. Here, we bridge a current gap in the mathematical modeling of infectious diseases and develop a framework that allows to account simultaneously for both the connectivity of individuals and the age-structure of the population. We compare different scenarios, namely, i) the homogeneous mixing setting, ii) one in which only the social mixing is taken into account, iii) a setting that considers the connectivity of individuals alone, and finally, iv) a multilayer representation in which both the social mixing and the number of contacts are included in the model. We analytically show that the thresholds obtained for these four scenarios are different. In addition, we conduct extensive numerical simulations and conclude that heterogeneities in the contact network are important for a proper determination of the epidemic threshold, whereas the age-structure plays a bigger role beyond the onset of the outbreak. Altogether, when it comes to evaluate interventions such as vaccination, both sources of individual heterogeneity are important and should be concurrently considered. Our results also provide an indication of the errors incurred in situations in which one cannot access all needed information in terms of connectivity and age of the population.

Measurability of the epidemic reproduction number in data-driven contact networks.

The basic reproduction number is one of the conceptual cornerstones of mathematical epidemiology. Its classical definition as the number of secondary cases generated by a typical infected individual in a fully susceptible population finds a clear analytical expression in homogeneous and stratified mixing models. Along with the generation time (the interval between primary and secondary cases), the reproduction number allows for the characterization of the dynamics of an epidemic. A clear-cut theoretical picture, however, is hardly found in real data. Here, we infer from highly detailed sociodemographic data two multiplex contact networks representative of a subset of the Italian and Dutch populations. We then simulate an infection transmission process on these networks accounting for the natural history of influenza and calibrated on empirical epidemiological data. We explicitly measure the reproduction number and generation time, recording all individual-level transmission events. We find that the classical concept of the basic reproduction number is untenable in realistic populations, and it does not provide any conceptual understanding of the epidemic evolution. This departure from the classical theoretical picture is not due to behavioral changes and other exogenous epidemiological determinants. Rather, it can be simply explained by the (clustered) contact structure of the population. Finally, we provide evidence that methodologies aimed at estimating the instantaneous reproduction number can operationally be used to characterize the correct epidemic dynamics from incidence data.

Data-driven model for the assessment of Mycobacterium tuberculosis transmission in evolving demographic structures.

In the case of tuberculosis (TB), the capabilities of epidemic models to produce quantitatively robust forecasts are limited by multiple hindrances. Among these, understanding the complex relationship between disease epidemiology and populations' age structure has been highlighted as one of the most relevant. TB dynamics depends on age in multiple ways, some of which are traditionally simplified in the literature. That is the case of the heterogeneities in contact intensity among different age strata that are common to all airborne diseases, but still typically neglected in the TB case. Furthermore, while demographic structures of many countries are rapidly aging, demographic dynamics are pervasively ignored when modeling TB spreading. In this work, we present a TB transmission model that incorporates country-specific demographic prospects and empirical contact data around a data-driven description of TB dynamics. Using our model, we find that the inclusion of demographic dynamics is followed by an increase in the burden levels predicted for the next decades in the areas of the world that are most hit by the disease today. Similarly, we show that considering realistic patterns of contacts among individuals in different age strata reshapes the transmission patterns reproduced by the models, a result with potential implications for the design of age-focused epidemiological interventions.

Evaluation of the potential incidence of COVID-19 and effectiveness of containment measures in Spain: a data-driven approach.

BACKGROUND: We are currently experiencing an unprecedented challenge, managing and containing an outbreak of a new coronavirus disease known as COVID-19. While China-where the outbreak started-seems to have been able to contain the growth of the epidemic, different outbreaks are nowadays present in multiple countries. Nonetheless, authorities have taken action and implemented containment measures, even if not everything is known. METHODS: To facilitate this task, we have studied the effect of different containment strategies that can be put into effect. Our work referred initially to the situation in Spain as of February 28, 2020, where a few dozens of cases had been detected, but has been updated to match the current situation as of 13 April. We implemented an SEIR metapopulation model that allows tracing explicitly the spatial spread of the disease through data-driven stochastic simulations. RESULTS: Our results are in line with the most recent recommendations from the World Health Organization, namely, that the best strategy is the early detection and isolation of individuals with symptoms, followed by interventions and public recommendations aimed at reducing the transmissibility of the disease, which, although might not be sufficient for disease eradication, would produce as a second order effect a delay of several days in the raise of the number of infected cases. CONCLUSIONS: Many quantitative aspects of the natural history of the disease are still unknown, such as the amount of possible asymptomatic spreading or the role of age in both the susceptibility and mortality of the disease. However, preparedness plans and mitigation interventions should be ready for quick and efficacious deployment globally. The scenarios evaluated here through data-driven simulations indicate that measures aimed at reducing individuals' flow are much less effective than others intended for early case identification and isolation. Therefore, resources should be directed towards detecting as many and as fast as possible the new cases and isolate them.

Unsupervised extraction of epidemic syndromes from participatory influenza surveillance self-reported symptoms.

Seasonal influenza surveillance is usually carried out by sentinel general practitioners (GPs) who compile weekly reports based on the number of influenza-like illness (ILI) clinical cases observed among visited patients. This traditional practice for surveillance generally presents several issues, such as a delay of one week or more in releasing reports, population biases in the health-seeking behaviour, and the lack of a common definition of ILI case. On the other hand, the availability of novel data streams has recently led to the emergence of non-traditional approaches for disease surveillance that can alleviate these issues. In Europe, a participatory web-based surveillance system called Influenzanet represents a powerful tool for monitoring seasonal influenza epidemics thanks to aid of self-selected volunteers from the general population who monitor and report their health status through Internet-based surveys, thus allowing a real-time estimate of the level of influenza circulating in the population. In this work, we propose an unsupervised probabilistic framework that combines time series analysis of self-reported symptoms collected by the Influenzanet platforms and performs an algorithmic detection of groups of symptoms, called syndromes. The aim of this study is to show that participatory web-based surveillance systems are capable of detecting the temporal trends of influenza-like illness even without relying on a specific case definition. The methodology was applied to data collected by Influenzanet platforms over the course of six influenza seasons, from 2011-2012 to 2016-2017, with an average of 34,000 participants per season. Results show that our framework is capable of selecting temporal trends of syndromes that closely follow the ILI incidence rates reported by the traditional surveillance systems in the various countries (Pearson correlations ranging from 0.69 for Italy to 0.88 for the Netherlands, with the sole exception of Ireland with a correlation of 0.38). The proposed framework was able to forecast quite accurately the ILI trend of the forthcoming influenza season (2016-2017) based only on the available information of the previous years (2011-2016). Furthermore, to broaden the scope of our approach, we applied it both in a forecasting fashion to predict the ILI trend of the 2016-2017 influenza season (Pearson correlations ranging from 0.60 for Ireland and UK, and 0.85 for the Netherlands) and also to detect gastrointestinal syndrome in France (Pearson correlation of 0.66). The final result is a near-real-time flexible surveillance framework not constrained by any specific case definition and capable of capturing the heterogeneity in symptoms circulation during influenza epidemics in the various European countries.

Effect of memory, intolerance, and second-order reputation on cooperation.

The understanding of cooperative behavior in social systems has been the subject of intense research over the past few decades. In this regard, the theoretical models used to explain cooperation in human societies have been complemented with a growing interest in experimental studies to validate the proposed mechanisms. In this work, we rely on previous experimental findings to build a theoretical model based on two cooperation driving mechanisms: second-order reputation and memory. Specifically, taking the donation game as a starting point, the agents are distributed among three strategies, namely, unconditional cooperators, unconditional defectors, and discriminators, where the latter follow a second-order assessment rule: shunning, stern judging, image scoring, or simple standing. A discriminator will cooperate if the evaluation of the recipient's last actions contained in his memory is above a threshold of (in)tolerance. In addition to the dynamics inherent to the game, another imitation dynamics, involving much longer times (generations), is introduced. The model is approached through a mean-field approximation that predicts the macroscopic behavior observed in Monte Carlo simulations. We found that, while in most second-order assessment rules, intolerance hinders cooperation, it has the opposite (positive) effect under the simple standing rule. Furthermore, we show that, when considering memory, the stern judging rule shows the lowest values of cooperation, while stricter rules show higher cooperation levels.

A data-driven assessment of early travel restrictions related to the spreading of the novel COVID-19 within mainland China.

Two months after it was firstly reported, the novel coronavirus disease COVID-19 spread worldwide. However, the vast majority of reported infections until February occurred in China. To assess the effect of early travel restrictions adopted by the health authorities in China, we have implemented an epidemic metapopulation model that is fed with mobility data corresponding to 2019 and 2020. This allows to compare two radically different scenarios, one with no travel restrictions and another in which mobility is reduced by a travel ban. Our findings indicate that i) travel restrictions might be an effective measure in the short term, however, ii) they are ineffective when it comes to completely eliminate the disease. The latter is due to the impossibility of removing the risk of seeding the disease to other regions. Furthermore, our study highlights the importance of developing more realistic models of behavioral changes when a disease outbreak is unfolding.

Projecting social contact matrices to different demographic structures.

The modeling of large-scale communicable epidemics has greatly benefited in the last years from the increasing availability of highly detailed data. Particullarly, in order to achieve quantitative descriptions of the evolution of epidemics, contact networks and mixing patterns are key. These heterogeneous patterns depend on several factors such as location, socioeconomic conditions, time, and age. This last factor has been shown to encapsulate a large fraction of the observed inter-individual variation in contact patterns, an observation validated by different measurements of age-dependent contact matrices. Recently, several works have studied how to project those matrices to areas where empirical data are not available. However, the dependence of contact matrices on demographic structures and their time evolution has been largely neglected. In this work, we tackle the problem of how to transform an empirical contact matrix that has been obtained for a given demographic structure into a different contact matrix that is compatible with a different demography. The methodology discussed here allows to extrapolate a contact structure measured in a particular area to any other whose demographic structure is known, as well as to obtain the time evolution of contact matrices as a function of the demographic dynamics of the populations they refer to. To quantify the effect of considering time-dynamics of contact patterns on disease modeling, we implemented a Susceptible-Exposed-Infected-Recovered (SEIR) model on 16 different countries and regions and evaluated the impact of neglecting the temporal evolution of mixing patterns. Our results show that simulated disease incidence rates, both at the aggregated and age-specific levels, are significantly dependent on contact structures variation driven by demographic evolution. The present work opens the path to eliminate technical biases from model-based impact evaluations of future epidemic threats and warns against the use of contact matrices to model diseases without correcting for demographic evolution or geographic variations.

Sparse Power-Law Network Model for Reliable Statistical Predictions Based on Sampled Data.

A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model that does not depend on the order in which nodes are sampled. Despite a large variety of non-equilibrium (growing) and equilibrium (static) sparse complex network models that are widely used in network science, how to reconcile sparseness (constant average degree) with the desired statistical properties of projectivity and exchangeability is currently an outstanding scientific problem. Here we propose a network process with hidden variables which is projective and can generate sparse power-law networks. Despite the model not being exchangeable, it can be closely related to exchangeable uncorrelated networks as indicated by its information theory characterization and its network entropy. The use of the proposed network process as a null model is here tested on real data, indicating that the model offers a promising avenue for statistical network modelling.

Unfolding the Complexity of the Global Value Chain: Strength and Entropy in the Single-Layer, Multiplex, and Multi-Layer International Trade Networks.

The worldwide trade network has been widely studied through different data sets and network representations with a view to better understanding interactions among countries and products. Here we investigate international trade through the lenses of the single-layer, multiplex, and multi-layer networks. We discuss differences among the three network frameworks in terms of their relative advantages in capturing salient topological features of trade. We draw on the World Input-Output Database to build the three networks. We then uncover sources of heterogeneity in the way strength is allocated among countries and transactions by computing the strength distribution and entropy in each network. Additionally, we trace how entropy evolved, and show how the observed peaks can be associated with the onset of the global economic downturn. Findings suggest how more complex representations of trade, such as the multi-layer network, enable us to disambiguate the distinct roles of intra- and cross-industry transactions in driving the evolution of entropy at a more aggregate level. We discuss our results and the implications of our comparative analysis of networks for research on international trade and other empirical domains across the natural and social sciences.

Participatory Syndromic Surveillance of Influenza in Europe.

The growth of digital communication technologies for public health is offering an unconventional means to engage the general public in monitoring community health. Here we present Influenzanet, a participatory system for the syndromic surveillance of influenza-like illness (ILI) in Europe. Through standardized online surveys, the system collects detailed profile information and self-reported symptoms volunteered by participants resident in the Influenzanet countries. Established in 2009, it now includes 10 countries representing more than half of the 28 member states of the European Union population. The experience of 7 influenza seasons illustrates how Influenzanet has become an adjunct to existing ILI surveillance networks, offering coherence across countries, inclusion of nonmedically attended ILI, flexibility in case definition, and facilitating individual-level epidemiological analyses generally not possible in standard systems. Having the sensitivity to timely detect substantial changes in population health, Influenzanet has the potential to become a viable instrument for a wide variety of applications in public health preparedness and control.

Heterogeneous networks do not promote cooperation when humans play a Prisoner's Dilemma.

It is not fully understood why we cooperate with strangers on a daily basis. In an increasingly global world, where interaction networks and relationships between individuals are becoming more complex, different hypotheses have been put forward to explain the foundations of human cooperation on a large scale and to account for the true motivations that are behind this phenomenon. In this context, population structure has been suggested to foster cooperation in social dilemmas, but theoretical studies of this mechanism have yielded contradictory results so far; additionally, the issue lacks a proper experimental test in large systems. We have performed the largest experiments to date with humans playing a spatial Prisoner's Dilemma on a lattice and a scale-free network (1,229 subjects). We observed that the level of cooperation reached in both networks is the same, comparable with the level of cooperation of smaller networks or unstructured populations. We have also found that subjects respond to the cooperation that they observe in a reciprocal manner, being more likely to cooperate if, in the previous round, many of their neighbors and themselves did so, which implies that humans do not consider neighbors' payoffs when making their decisions in this dilemma but only their actions. Our results, which are in agreement with recent theoretical predictions based on this behavioral rule, suggest that population structure has little relevance as a cooperation promoter or inhibitor among humans.

Host mobility drives pathogen competition in spatially structured populations.

Interactions among multiple infectious agents are increasingly recognized as a fundamental issue in the understanding of key questions in public health regarding pathogen emergence, maintenance, and evolution. The full description of host-multipathogen systems is, however, challenged by the multiplicity of factors affecting the interaction dynamics and the resulting competition that may occur at different scales, from the within-host scale to the spatial structure and mobility of the host population. Here we study the dynamics of two competing pathogens in a structured host population and assess the impact of the mobility pattern of hosts on the pathogen competition. We model the spatial structure of the host population in terms of a metapopulation network and focus on two strains imported locally in the system and having the same transmission potential but different infectious periods. We find different scenarios leading to competitive success of either one of the strain or to the codominance of both strains in the system. The dominance of the strain characterized by the shorter or longer infectious period depends exclusively on the structure of the population and on the the mobility of hosts across patches. The proposed modeling framework allows the integration of other relevant epidemiological, environmental and demographic factors, opening the path to further mathematical and computational studies of the dynamics of multipathogen systems.