Filter bubble effect in the multistate voter model.

Social media influence online activity by recommending to users content strongly correlated with what they have preferred in the past. In this way, they constrain users within filter bubbles strongly limiting their exposure to new or alternative content. We investigate this type of dynamics by considering a multistate voter model where, with a given probability λ, a user interacts with "personalized information," suggesting the opinion most frequently held in the past. By means of theoretical arguments and numerical simulations, we show the existence of a nontrivial transition between a region (for small λ) where a consensus is reached and a region (above a threshold λc) where the system gets polarized and clusters of users with different opinions persist indefinitely. The threshold always vanishes for large system size N, showing that a consensus becomes impossible for a large number of users. This finding opens new questions about the side effects of the widespread use of personalized recommendation algorithms.

Message-passing theory for cooperative epidemics.

The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the phenomenology of epidemic spreading, leading, for instance, to abrupt transitions and hysteresis. Here, we consider a simple model for two interacting pathogens on a network and we study it by using the message-passing approach. In this way, we are able to provide detailed predictions for the behavior of the model in the whole phase-diagram for any given network structure. Numerical simulations on synthetic networks (both homogeneous and heterogeneous) confirm the great accuracy of the theoretical results. We finally consider the issue of identifying the nodes where it is better to seed the infection in order to maximize the probability of observing an extensive outbreak. The message-passing approach provides an accurate solution also for this problem.

Uncertainty Reduction for Stochastic Processes on Complex Networks.

Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the stochastic rules, the ability to predict system configurations is generally characterized by a large uncertainty. Selecting a fraction of the nodes and observing their state may help to reduce the uncertainty about the unobserved nodes. However, choosing these points of observation in an optimal way is a highly nontrivial task, depending on the nature of the stochastic process and on the structure of the underlying interaction pattern. In this paper, we introduce a computationally efficient algorithm to determine quasioptimal solutions to the problem. The method leverages network sparsity to reduce computational complexity from exponential to almost quadratic, thus allowing the straightforward application of the method to mid-to-large-size systems. Although the method is exact only for equilibrium stochastic processes defined on trees, it turns out to be effective also for out-of-equilibrium processes on sparse loopy networks.

Strongly clustered random graphs via triadic closure: An exactly solvable model.

Triadic closure, the formation of a connection between two nodes in a network sharing a common neighbor, is considered a fundamental mechanism determining the clustered nature of many real-world topologies. In this work we define a static triadic closure (STC) model for clustered networks, whereby starting from an arbitrary fixed backbone network, each triad is closed independently with a given probability. Assuming a locally treelike backbone we derive exact expressions for the expected number of various small, loopy motifs (triangles, 4-loops, diamonds, and 4-cliques) as a function of moments of the backbone degree distribution. In this way we determine how transitivity and its suitably defined generalizations for higher-order motifs depend on the heterogeneity of the original network, revealing the existence of transitions due to the interplay between topologically inequivalent triads in the network. Furthermore, under reasonable assumptions for the moments of the backbone network, we establish approximate relationships between motif densities, which we test in a large dataset of real-world networks. We find a good agreement, indicating that STC is a realistic mechanism for the generation of clustered networks, while remaining simple enough to be amenable to analytical treatment.

Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks.

We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.

Extended-range percolation in complex networks.

Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted path of nodes between them. In a variety of more recent data transmission protocols, such as the communication of noisy data via error-correcting repeaters, both in classical and quantum networks, the requirement of an uninterrupted path is too strict: two nodes may be able to communicate even if all paths between them have interruptions or gaps consisting of nodes that may corrupt the message. In such a case a different approach is needed. We develop the theoretical framework for extended-range percolation in networks, describing the fundamental connectivity properties relevant to such models of information transfer. We obtain exact results, for any range R, for infinite random uncorrelated networks and we provide a message-passing formulation that works well in sparse real-world networks. The interplay of the extended range and heterogeneity leads to novel critical behavior in scale-free networks.

Limited efficacy of forward contact tracing in epidemics.

Infectious diseases that spread silently through asymptomatic or pre-symptomatic infections represent a challenge for policy makers. A traditional way of achieving isolation of silent infectors from the community is through forward contact tracing, aimed at identifying individuals that might have been infected by a known infected person. In this work we investigate how efficient this measure is in preventing a disease from becoming endemic. We introduce an SIS-based compartmental model where symptomatic individuals may self-isolate and trigger a contact tracing process aimed at quarantining asymptomatic infected individuals. Imperfect adherence and delays affect both measures. We derive the epidemic threshold analytically and find that contact tracing alone can only lead to a very limited increase of the threshold. We quantify the effect of imperfect adherence and the impact of incentivizing asymptomatic and symptomatic populations to adhere to isolation. Our analytical results are confirmed by simulations on complex networks and by the numerical analysis of a much more complex model incorporating more realistic in-host disease progression.

Critical avalanches of susceptible-infected-susceptible dynamics in finite networks.

We investigate the avalanche temporal statistics of the susceptible-infected-susceptible (SIS) model when the dynamics is critical and takes place on finite random networks. By considering numerical simulations on annealed topologies we show that the survival probability always exhibits three distinct dynamical regimes. Size-dependent crossover timescales separating them scale differently for homogeneous and for heterogeneous networks. The phenomenology can be qualitatively understood based on known features of the SIS dynamics on networks. A fully quantitative approach based on Langevin theory is shown to perfectly reproduce the results for homogeneous networks, while failing in the heterogeneous case. The analysis is extended to quenched random networks, which behave in agreement with the annealed case for strongly homogeneous and strongly heterogeneous networks.

Effect of collaborative-filtering-based recommendation algorithms on opinion polarization.

A central role in shaping the experience of users online is played by recommendation algorithms. On the one hand they help retrieving content that best suits users taste, but on the other hand they may give rise to the so-called "filter bubble" effect, favoring the rise of polarization. In the present paper we study how a user-user collaborative-filtering algorithm affects the behavior of a group of agents repeatedly exposed to it. By means of analytical and numerical techniques we show how the system stationary state depends on the strength of the similarity and popularity biases, quantifying respectively the weight given to the most similar users and to the best rated items. In particular, we derive a phase diagram of the model, where we observe three distinct phases: disorder, consensus, and polarization. In the last users spontaneously split into different groups, each focused on a single item. We identify, at the boundary between the disorder and polarization phases, a region where recommendations are nontrivially personalized without leading to filter bubbles. Finally, we show that our model well reproduces the behavior of users on the online music platform last.fm. This analysis paves the way to a systematic analysis of recommendation algorithms by means of statistical physics methods and opens the possibility of devising less polarizing recommendation algorithms.

Attitudes towards booster, testing and isolation, and their impact on COVID-19 response in winter 2022/2023 in France, Belgium, and Italy: a cross-sectional survey and modelling study.

Background: European countries are focusing on testing, isolation, and boosting strategies to counter the 2022/2023 winter surge due to SARS-CoV-2 Omicron subvariants. However, widespread pandemic fatigue and limited compliance potentially undermine mitigation efforts. Methods: To establish a baseline for interventions, we ran a multicountry survey to assess respondents' willingness to receive booster vaccination and comply with testing and isolation mandates. Integrating survey and estimated immunity data in a branching process epidemic spreading model, we evaluated the effectiveness and costs of current protocols in France, Belgium, and Italy to manage the winter wave. Findings: The vast majority of survey participants (N = 4594) was willing to adhere to testing (>91%) and rapid isolation (>88%) across the three countries. Pronounced differences emerged in the declared senior adherence to booster vaccination (73% in France, 94% in Belgium, 86% in Italy). Epidemic model results estimate that testing and isolation protocols would confer significant benefit in reducing transmission (17-24% reduction, from R = 1.6 to R = 1.3 in France and Belgium, to R = 1.2 in Italy) with declared adherence. Achieving a mitigating level similar to the French protocol, the Belgian protocol would require 35% fewer tests (from 1 test to 0.65 test per infected person) and avoid the long isolation periods of the Italian protocol (average of 6 days vs. 11). A cost barrier to test would significantly decrease adherence in France and Belgium, undermining protocols' effectiveness. Interpretation: Simpler mandates for isolation may increase awareness and actual compliance, reducing testing costs, without compromising mitigation. High booster vaccination uptake remains key for the control of the winter wave. Funding: The European Commission, ANRS-Maladies Infectieuses Émergentes, the Agence Nationale de la Recherche, the Chaires Blaise Pascal Program of the Île-de-France region.

The advantage of self-protecting interventions in mitigating epidemic circulation at the community level.

Protecting interventions of many types (both pharmaceutical and non-pharmaceutical) can be deployed against the spreading of a communicable disease, as the worldwide COVID-19 pandemic has dramatically shown. Here we investigate in detail the effects at the population level of interventions that provide an asymmetric protection between the people involved in a single interaction. Masks of different filtration types, either protecting mainly the wearer or the contacts of the wearer, are a prominent example of these interventions. By means of analytical calculations and extensive simulations of simple epidemic models on networks, we show that interventions protecting more efficiently the adopter (e.g the mask wearer) are more effective than interventions protecting primarily the contacts of the adopter in reducing the prevalence of the disease and the number of concurrently infected individuals ("flattening the curve"). This observation is backed up by the study of a more realistic epidemic model on an empirical network representing the patterns of contacts in the city of Portland. Our results point out that promoting wearer-protecting face masks and other self-protecting interventions, though deemed selfish and inefficient, can actually be a better strategy to efficiently curtail pandemic spreading.

Cumulative merging percolation: A long-range percolation process in networks.

Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they are nearest neighbors. Cumulative merging percolation (CMP) is a percolation process that assumes long-range interactions such that nodes can merge into clusters even if they are topologically distant. Hence, in CMP clusters do not coincide with the topologically connected components of the network. Previous work has shown that a specific formulation of CMP features peculiar mechanisms for the formation of the giant cluster and allows one to model different network dynamics such as recurrent epidemic processes. Here we develop a more general formulation of CMP in terms of the functional form of the cluster interaction range, showing an even richer phase transition scenario with competition of different mechanisms resulting in crossover phenomena. Our analytic predictions are confirmed by numerical simulations.

Sideward contact tracing and the control of epidemics in large gatherings.

Effective contact tracing is crucial to containing epidemic spreading without disrupting societal activities, especially during a pandemic. Large gatherings play a key role, potentially favouring superspreading events. However, the effects of tracing in large groups have not been fully assessed so far. We show that in addition to forward tracing, which reconstructs to whom the disease spreads, and backward tracing, which searches from whom the disease spreads, a third 'sideward' tracing is always present, when tracing gatherings. This is an indirect tracing that detects infected asymptomatic individuals, even if they have been neither directly infected by nor directly transmitted the infection to the index case. We analyse this effect in a model of epidemic spreading for SARS-CoV-2, within the framework of simplicial activity-driven temporal networks. We determine the contribution of the three tracing mechanisms to the suppression of epidemic spreading, showing that sideward tracing induces a non-monotonic behaviour in the tracing efficiency, as a function of the size of the gatherings. Based on our results, we suggest an optimal choice for the sizes of the gatherings to be traced and we test the strategy on an empirical dataset of gatherings on a university campus.

Universality, criticality and complexity of information propagation in social media.

Statistical laws of information avalanches in social media appear, at least according to existing empirical studies, not robust across systems. As a consequence, radically different processes may represent plausible driving mechanisms for information propagation. Here, we analyze almost one billion time-stamped events collected from several online platforms - including Telegram, Twitter and Weibo - over observation windows longer than ten years, and show that the propagation of information in social media is a universal and critical process. Universality arises from the observation of identical macroscopic patterns across platforms, irrespective of the details of the specific system at hand. Critical behavior is deduced from the power-law distributions, and corresponding hyperscaling relations, characterizing size and duration of avalanches of information. Statistical testing on our data indicates that a mixture of simple and complex contagion characterizes the propagation of information in social media. Data suggest that the complexity of the process is correlated with the semantic content of the information that is propagated.

Universality of citation distributions: toward an objective measure of scientific impact.

We study the distributions of citations received by a single publication within several disciplines, spanning broad areas of science. We show that the probability that an article is cited c times has large variations between different disciplines, but all distributions are rescaled on a universal curve when the relative indicator c(f) = c/c(0) is considered, where c(0) is the average number of citations per article for the discipline. In addition we show that the same universal behavior occurs when citation distributions of articles published in the same field, but in different years, are compared. These findings provide a strong validation of c(f) as an unbiased indicator for citation performance across disciplines and years. Based on this indicator, we introduce a generalization of the h index suitable for comparing scientists working in different fields.

Influence of individual nodes for continuous-time susceptible-infected-susceptible dynamics on synthetic and real-world networks.

In the study of epidemic dynamics a fundamental question is whether a pathogen initially affecting only one individual will give rise to a limited outbreak or to a widespread pandemic. The answer to this question crucially depends not only on the parameters describing the infection and recovery processes but also on where, in the network of interactions, the infection starts from. We study the dependence on the location of the initial seed for the susceptible-infected-susceptible epidemic dynamics in continuous time on networks. We first derive analytical predictions for the dependence on the initial node of three indicators of spreading influence (probability to originate an infinite outbreak, average duration, and size of finite outbreaks) and compare them with numerical simulations on random uncorrelated networks, finding a very good agreement. We then show that the same theoretical approach works fairly well also on a set of real-world topologies of diverse nature. We conclude by briefly investigating which topological network features determine deviations from the theoretical predictions.

Stochastic sampling effects favor manual over digital contact tracing.

Isolation of symptomatic individuals, tracing and testing of their nonsymptomatic contacts are fundamental strategies for mitigating the current COVID-19 pandemic. The breaking of contagion chains relies on two complementary strategies: manual reconstruction of contacts based on interviews and a digital (app-based) privacy-preserving contact tracing. We compare their effectiveness using model parameters tailored to describe SARS-CoV-2 diffusion within the activity-driven model, a general empirically validated framework for network dynamics. We show that, even for equal probability of tracing a contact, manual tracing robustly performs better than the digital protocol, also taking into account the intrinsic delay and limited scalability of the manual procedure. This result is explained in terms of the stochastic sampling occurring during the case-by-case manual reconstruction of contacts, contrasted with the intrinsically prearranged nature of digital tracing, determined by the decision to adopt the app or not by each individual. The better performance of manual tracing is enhanced by heterogeneity in agent behavior: superspreaders not adopting the app are completely invisible to digital contact tracing, while they can be easily traced manually, due to their multiple contacts. We show that this intrinsic difference makes the manual procedure dominant in realistic hybrid protocols.

Percolation theory of self-exciting temporal processes.

We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of microscopic events produced by a self-exciting Hawkes process, and leverage a percolation framework to study the formation of macroscopic bursts of activity as a function of the resolution parameter. We find that the very same process may result in different distributions of avalanche size and duration, which are understood in terms of the competition between the 1D percolation and the branching process universality class. Pure regimes for the individual classes are observed at specific values of the resolution parameter corresponding to the critical points of the percolation diagram. A regime of crossover characterized by a mixture of the two universal behaviors is observed in a wide region of the diagram. The hybrid scaling appears to be a likely outcome for an analysis of the time series based on a reasonably chosen, but not precisely adjusted, value of the resolution parameter.

Effect of delayed awareness and fatigue on the efficacy of self-isolation in epidemic control.

The isolation of infectious individuals is a key measure of public health for the control of communicable diseases. However, involving a strong perturbation of daily life, it often causes psychosocial distress, and severe financial and social costs. These may act as mechanisms limiting the adoption of the measure in the first place or the adherence throughout its full duration. In addition, difficulty of recognizing mild symptoms or lack of symptoms may impact awareness of the infection and further limit adoption. Here we study an epidemic model on a network of contacts accounting for limited adherence and delayed awareness to self-isolation, along with fatigue causing overhasty termination. The model allows us to estimate the role of each ingredient and analyze the tradeoff between adherence and duration of self-isolation. We find that the epidemic threshold is very sensitive to an effective compliance that combines the effects of imperfect adherence, delayed awareness and fatigue. If adherence improves for shorter quarantine periods, there exists an optimal duration of isolation, shorter than the infectious period. However, heterogeneities in the connectivity pattern, coupled to a reduced compliance for highly active individuals, may almost completely offset the effectiveness of self-isolation measures on the control of the epidemic.

Thresholds for epidemic spreading in networks.

We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible model the activity threshold λ(c) vanishes in the large size limit on any network whose maximum degree k(max) diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has nothing to do with the scale-free nature of the network but stems instead from the largest hub in the system being active for any spreading rate λ>1/√k(max) and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.