Epidemic spreading on activity-driven networks with attractiveness

(ω_{1},ω_{2})-temporal random hyperbolic graphs

We extend a recent model of temporal random hyperbolic graphs by allowing connections and disconnections to persist across network snapshots with different probabilities ω_{1} and ω_{2}. This extension, while conceptually simple, poses analytical challenges involving the Appell F_{1} series. Despite these challenges, we are able to analyze key properties of the model, which include the distributions of contact and intercontact durations, as well as the expected time-aggregated degree. The incorporation of ω_{1} and ω_{2} enables more flexible tuning of the average contact and intercontact durations, and of the average time-aggregated degree, providing a finer control for exploring the effect of temporal network dynamics on dynamical processes. Overall, our results provide new insights into the analysis of temporal networks and contribute to a more general representation of real-world scenarios.

Probabilistic activity driven model of temporal simplicial networks and its application on higher-order dynamics

Network modeling characterizes the underlying principles of structural properties and is of vital significance for simulating dynamical processes in real world. However, bridging structure and dynamics is always challenging due to the multiple complexities in real systems. Here, through introducing the individual's activity rate and the possibility of group interaction, we propose a probabilistic activity-driven (PAD) model that could generate temporal higher-order networks with both power-law and high-clustering characteristics, which successfully links the two most critical structural features and a basic dynamical pattern in extensive complex systems. Surprisingly, the power-law exponents and the clustering coefficients of the aggregated PAD network could be tuned in a wide range by altering a set of model parameters. We further provide an approximation algorithm to select the proper parameters that can generate networks with given structural properties, the effectiveness of which is verified by fitting various real-world networks. Finally, we construct the co-evolution framework of the PAD model and higher-order contagion dynamics and derive the critical conditions for phase transition and bistable phenomenon using theoretical and numerical methods. Results show that tendency of participating in higher-order interactions can promote the emergence of bistability but delay the outbreak under heterogeneous activity rates. Our model provides a basic tool to reproduce complex structural properties and to study the widespread higher-order dynamics, which has great potential for applications across fields.

A coupled awareness-epidemic model on a multi-layer time-varying network

Social interactions have become more complicated and changeable under the influence of information technology revolution. We, thereby, propose a multi-layer activity-driven network with attractiveness considering the heterogeneity of activated individual edge numbers, which aims to explore the role of heterogeneous behaviors in the time-varying network. Specifically, three types of individual behaviors are introduced: (i) self-quarantine of infected individuals, (ii) safe social distancing between infected and susceptible individuals, and (iii) information spreading of aware individuals. Epidemic threshold is theoretically derived in terms of the microscopic Markov chain approach and the mean-field approach. The results demonstrate that performing self-quarantine and maintaining safe social distance can effectively raise the epidemic threshold and suppress the spread of diseases. Interestingly, individuals' activity and individuals' attractiveness have an equivalent effect on epidemic threshold under the same condition. In addition, a similar result can be obtained regardless of the activated individual edge numbers. The epidemic outbreak earlier in a situation of the stronger heterogeneity of activated individual edge numbers.

Dynamics of cold random hyperbolic graphs with link persistence

We consider and analyze a dynamic model of random hyperbolic graphs with link persistence. In the model, both connections and disconnections can be propagated from the current to the next snapshot with probability ω∈[0,1). Otherwise, with probability 1-ω, connections are reestablished according to the random hyperbolic graphs model. We show that while the persistence probability ω affects the averages of the contact and intercontact distributions, it does not affect the tails of these distributions, which decay as power laws with exponents that do not depend on ω. We also consider examples of real temporal networks, and we show that the considered model can adequately reproduce several of their dynamical properties. Our results advance our understanding of the realistic modeling of temporal networks and of the effects of link persistence on temporal network properties.

Activity-driven network modeling and control of the spread of two concurrent epidemic strains

The emergency generated by the current COVID-19 pandemic has claimed millions of lives worldwide. There have been multiple waves across the globe that emerged as a result of new variants, due to arising from unavoidable mutations. The existing network toolbox to study epidemic spreading cannot be readily adapted to the study of multiple, coexisting strains. In this context, particularly lacking are models that could elucidate re-infection with the same strain or a different strain-phenomena that we are seeing experiencing more and more with COVID-19. Here, we establish a novel mathematical model to study the simultaneous spreading of two strains over a class of temporal networks. We build on the classical susceptible-exposed-infectious-removed model, by incorporating additional states that account for infections and re-infections with multiple strains. The temporal network is based on the activity-driven network paradigm, which has emerged as a model of choice to study dynamic processes that unfold at a time scale comparable to the network evolution. We draw analytical insight from the dynamics of the stochastic network systems through a mean-field approach, which allows for characterizing the onset of different behavioral phenotypes (non-epidemic, epidemic, and endemic). To demonstrate the practical use of the model, we examine an intermittent stay-at-home containment strategy, in which a fraction of the population is randomly required to isolate for a fixed period of time.

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.

Impact of individual behavioral changes on epidemic spreading in time-varying networks

Changes in individual behavior often entangle with the dynamic interaction of individuals, which complicates the epidemic process and brings great challenges for the understanding and control of the epidemic. In this work, we consider three kinds of typical behavioral changes in epidemic process, that is, self-quarantine of infected individuals, self-protection of susceptible individuals, and social distancing between them. We connect the behavioral changes with individual's social attributes by the activity-driven network with attractiveness. A mean-field theory is established to derive an analytical estimate of epidemic threshold for susceptible-infected-susceptible models with individual behavioral changes, which depends on the correlations between activity, attractiveness, and the number of generative links in the susceptible and infected states. We find that individual behaviors play different roles in suppressing the epidemic. Although all the behavioral changes could delay the epidemic by increasing the epidemic threshold, self-quarantine and social distancing of infected individuals could effectively decrease the epidemic outbreak size. In addition, simultaneous changes in these behaviors and the timing of implement of them also play a key role in suppressing the epidemic. These results provide helpful significance for understanding the interaction of individual behaviors in the epidemic process.

Game-theoretic modeling of collective decision making during epidemics

The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a parsimonious game-theoretic behavioral-epidemic model, in which an interplay of realistic factors shapes the coevolution of individual decision making and epidemics on a network. Although such a coevolution is deeply intertwined in the real world, existing models schematize population behavior as instantaneously reactive, thus being unable to capture human behavior in the long term. Our paradigm offers a unified framework to model and predict complex emergent phenomena, including successful collective responses, periodic oscillations, and resurgent epidemic outbreaks. The framework also allows us to provide analytical insights on the epidemic process and to assess the effectiveness of different policy interventions on ensuring a collective response that successfully eradicates the outbreak. Two case studies, inspired by real-world diseases, are presented to illustrate the potentialities of the proposed model.

UTLDR: an agent-based framework for modeling infectious diseases and public interventions

Due to the SARS-CoV-2 pandemic, epidemic modeling is now experiencing a constantly growing interest from researchers of heterogeneous study fields. Indeed, due to such an increased attention, several software libraries and scientific tools have been developed to ease the access to epidemic modeling. However, only a handful of such resources were designed with the aim of providing a simple proxy for the study of the potential effects of public interventions (e.g., lockdown, testing, contact tracing). In this work, we introduce UTLDR, a framework that, overcoming such limitations, allows to generate "what if" epidemic scenarios incorporating several public interventions (and their combinations). UTLDR is designed to be easy to use and capable to leverage information provided by stratified populations of agents (e.g., age, gender, geographical allocation, and mobility patterns…). Moreover, the proposed framework is generic and not tailored for a specific epidemic phenomena: it aims to provide a qualitative support to understanding the effects of restrictions, rather than produce forecasts/explanation of specific data-driven phenomena.

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.

How adherence to public health measures shapes epidemic spreading: A temporal network model

The COVID-19 pandemic has laid bare the importance of non-pharmaceutical interventions in the containment of airborne infectious diseases. Social distancing and mask-wearing have been found to contain COVID-19 spreading across a number of observational studies, but a precise understanding of their combined effectiveness is lacking. An underdeveloped area of research entails the quantification of the specific role of each of these measures when they are differentially adopted by the population. Pursuing this research allows for answering several pressing questions like: how many people should follow public health measures for them to be effective for everybody? Is it sufficient to practice social distancing only or just wear a mask? Here, we make a first step in this direction, by establishing a susceptible-exposed-infected-removed epidemic model on a temporal network, evolving according to the activity-driven paradigm. Through analytical and numerical efforts, we study epidemic spreading as a function of the proportion of the population following public health measures, the extent of social distancing, and the efficacy of masks in protecting the wearer and others. Our model demonstrates that social distancing and mask-wearing can be effective in preventing COVID-19 outbreaks if adherence to both measures involves a substantial fraction of the population.

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.

Network temporality can promote and suppress information spreading

Temporality is an essential characteristic of many real-world networks and dramatically affects the spreading dynamics on networks. In this paper, we propose an information spreading model on temporal networks with heterogeneous populations. Individuals are divided into activists and bigots to describe the willingness to accept the information. Through a developed discrete Markov chain approach and extensive numerical simulations, we discuss the phase diagram of the model and the effects of network temporality. From the phase diagram, we find that the outbreak phase transition is continuous when bigots are relatively rare, and a hysteresis loop emerges when there are a sufficient number of bigots. The network temporality does not qualitatively alter the phase diagram. However, we find that the network temporality affects the spreading outbreak size by either promoting or suppressing, which relies on the heterogeneities of population and of degree distribution. Specifically, in networks with homogeneous and weak heterogeneous degree distribution, the network temporality suppresses (promotes) the information spreading for small (large) values of information transmission probability. In networks with strong heterogeneous degree distribution, the network temporality always promotes the information spreading when activists dominate the population, or there are relatively fewer activists. Finally, we also find the optimal network evolution scale, under which the network information spreading is maximized.

Active and inactive quarantine in epidemic spreading on adaptive activity-driven networks

We consider an epidemic process on adaptive activity-driven temporal networks, with adaptive behavior modeled as a change in activity and attractiveness due to infection. By using a mean-field approach, we derive an analytical estimate of the epidemic threshold for susceptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) epidemic models for a general adaptive strategy, which strongly depends on the correlations between activity and attractiveness in the susceptible and infected states. We focus on strong social distancing, implementing two types of quarantine inspired by recent real case studies: an active quarantine, in which the population compensates the loss of links rewiring the ineffective connections towards nonquarantining nodes, and an inactive quarantine, in which the links with quarantined nodes are not rewired. Both strategies feature the same epidemic threshold but they strongly differ in the dynamics of the active phase. We show that the active quarantine is extremely less effective in reducing the impact of the epidemic in the active phase compared to the inactive one and that in the SIR model a late adoption of measures requires inactive quarantine to reach containment.

A multilayer temporal network model for STD spreading accounting for permanent and casual partners

Sexually transmitted diseases (STD) modeling has used contact networks to study the spreading of pathogens. Recent findings have stressed the increasing role of casual partners, often enabled by online dating applications. We study the Susceptible-Infected-Susceptible (SIS) epidemic model –appropriate for STDs– over a two-layer network aimed to account for the effect of casual partners in the spreading of STDs. In this novel model, individuals have a set of steady partnerships (links in layer 1). At certain rates, every individual can switch between active and inactive states and, while active, it establishes casual partnerships with some probability with active neighbors in layer 2 (whose links can be thought as potential casual partnerships). Individuals that are not engaged in casual partnerships are classified as inactive, and the transitions between active and inactive states are independent of their infectious state. We use mean-field equations as well as stochastic simulations to derive the epidemic threshold, which decreases substantially with the addition of the second layer. Interestingly, for a given expected number of casual partnerships, which depends on the probabilities of being active, this threshold turns out to depend on the duration of casual partnerships: the longer they are, the lower the threshold.

Containing misinformation spreading in temporal social networks

Many researchers from a variety of fields, including computer science, network science, and mathematics, have focused on how to contain the outbreaks of Internet misinformation that threaten social systems and undermine societal health. Most research on this topic treats the connections among individuals as static, but these connections change in time, and thus social networks are also temporal networks. Currently, there is no theoretical approach to the problem of containing misinformation outbreaks in temporal networks. We thus propose a misinformation spreading model for temporal networks and describe it using a new theoretical approach. We propose a heuristic-containing (HC) strategy based on optimizing the final outbreak size that outperforms simplified strategies such as those that are random-containing and targeted-containing. We verify the effectiveness of our HC strategy on both artificial and real-world networks by performing extensive numerical simulations and theoretical analyses. We find that the HC strategy dramatically increases the outbreak threshold and decreases the final outbreak threshold.

Epidemic spreading with awareness diffusion on activity-driven networks

Acknowledging the significance of awareness diffusion and behavioral response in contagion outbreaks has been regarded as an indispensable prerequisite for a complete understanding of epidemic spreading. Recent studies from the research community have accumulated overwhelming evidence for the incessantly evolving structure of the underlying networks. Thus there is an impelling need to capture the interplay between the epidemic spreading and awareness diffusion on time-varying networks. In this paper, we consider a behavioral model in which susceptible individuals become alert and adopt a preventive behavior under the local risk perception characterized by a decision-making threshold. The impact of awareness diffusion on the epidemic threshold is investigated under the framework of activity-driven network. Results show that the local epidemic situation in risk perception and the duration of preventive effect are crucial for raising the epidemic threshold. The analytical results are corroborated by Monte Carlo simulations.

Epidemic spreading and aging in temporal networks with memory

Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we analyze the combined effect of these two ingredients on epidemic dynamics on networks. We study the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered (SIR) models on the recently introduced activity-driven networks with memory. By means of an activity-based mean-field approach, we derive, in the long-time limit, analytical predictions for the epidemic threshold as a function of the parameters describing the distribution of activities and the strength of the memory effects. Our results show that memory reduces the threshold, which is the same for SIS and SIR dynamics, therefore favoring epidemic spreading. The theoretical approach perfectly agrees with numerical simulations in the long-time asymptotic regime. Strong aging effects are present in the preasymptotic regime and the epidemic threshold is deeply affected by the starting time of the epidemics. We discuss in detail the origin of the model-dependent preasymptotic corrections, whose understanding could potentially allow for epidemic control on correlated temporal networks.

Universal principles governing multiple random searchers on complex networks: The logarithmic growth pattern and the harmonic law

We propose a unified framework to evaluate and quantify the search time of multiple random searchers traversing independently and concurrently on complex networks. We find that the intriguing behaviors of multiple random searchers are governed by two basic principles-the logarithmic growth pattern and the harmonic law. Specifically, the logarithmic growth pattern characterizes how the search time increases with the number of targets, while the harmonic law explores how the search time of multiple random searchers varies relative to that needed by individual searchers. Numerical and theoretical results demonstrate these two universal principles established across a broad range of random search processes, including generic random walks, maximal entropy random walks, intermittent strategies, and persistent random walks. Our results reveal two fundamental principles governing the search time of multiple random searchers, which are expected to facilitate investigation of diverse dynamical processes like synchronization and spreading.

Epidemic spreading in modular time-varying networks

We investigate the effects of modular and temporal connectivity patterns on epidemic spreading. To this end, we introduce and analytically characterise a model of time-varying networks with tunable modularity. Within this framework, we study the epidemic size of Susceptible-Infected-Recovered, SIR, models and the epidemic threshold of Susceptible-Infected-Susceptible, SIS, models. Interestingly, we find that while the presence of tightly connected clusters inhibits SIR processes, it speeds up SIS phenomena. In this case, we observe that modular structures induce a reduction of the threshold with respect to time-varying networks without communities. We confirm the theoretical results by means of extensive numerical simulations both on synthetic graphs as well as on a real modular and temporal network.