Activity-driven Model Research Articles

Epidemic criticality in temporal networks

Analytical studies of network epidemiology almost exclusively focus on the extreme situations where the timescales of network dynamics are well separated (longer or shorter) from that of epidemic propagation. In realistic scenarios, however, these timescales could be similar, which has profound implications for epidemic modeling (e.g., one can no longer reduce the dimensionality of epidemic models). Combining Monte Carlo simulations and mean-field theory, we analyze the critical behavior of susceptible-infected-susceptible epidemics in the vicinity of the critical threshold on the activity-driven model of temporal networks. We find that the persistence of links in the network causes the threshold to decrease as the recovery rate increases. Dynamic correlations (coming from being close to infected nodes increases the likelihood of infection) drive the threshold in the opposite direction. These two counteracting effects make epidemic criticality in temporal networks a remarkably complex phenomenon. Published by the American Physical Society 2024

Impact of different interaction behavior on epidemic spreading in time-dependent social networks

We investigate the impact of pairwise and group interactions on the spread of epidemics through an activity-driven model based on time-dependent networks. The effects of pairwise/group interaction proportion and pairwise/group interaction intensity are explored by extensive simulation and theoretical analysis. It is demonstrated that altering the group interaction proportion can either hinder or enhance the spread of epidemics, depending on the relative social intensity of group and pairwise interactions. As the group interaction proportion decreases, the impact of reducing group social intensity diminishes. The ratio of group and pairwise social intensity can affect the effect of group interaction proportion on the scale of infection. A weak heterogeneous activity distribution can raise the epidemic threshold, and reduce the scale of infection. These results benefit the design of epidemic control strategy.

Rumor spreading in a dual-relationship network with diverse propagation abilities

The increasing number of online ties created on social platforms has made our social relations and influences more complex and diverse. This paper proposes a multilayer-like network model for rumor spreading that incorporates both strong and weak relations. Two types of fixed topologies are used to describe strong relations, while the activity-driven model is employed for weak relations. The model also takes into consideration the differential propagation abilities of individuals. The rumor spreading thresholds are theoretically derived using mean-field theory and an approximation method, which are consistent with simulation results. Results indicate that differences in individuals’ strong relations significantly influence rumor spreading. Specifically, when the strong relation structure is a heterogeneous network, the density of rumor spreaders reaches equilibrium in a shorter time, and the final density of rumor spreaders is higher. However, when the strong relation structure is a homogeneous network and individuals’ activity rates are negatively correlated with their propagation abilities, rumor spreading is easier. Interestingly, the opposite result is obtained when the strong relation structure is a heterogeneous network. Additionally, individuals’ propagation abilities and weak relations can affect the final density of rumor spreaders, but the effects are not identical.

Impact of different social attitudes on epidemic spreading in activity-driven networks

In human society, individual interactions intrinsically change, with profound implications for epidemics. The activity-driven model, a type of temporal network, offers an excellent framework to study epidemic processes in dynamical interaction. In this work, we study how social attitudes affect the transmission of infectious diseases in activity-driven networks. Here, we divide a population into “risk-ignorant” and “risk-averse”, in which risk-averse individuals will reduce their social intensity (Social intensity refers to the number of social contacts in the social process) and risk-ignorant individuals will not. A parameter p controls the proportion of risk-averse individuals, and therefore risk-ignorant individuals by 1-p. With the aid of mean-field theory, we calculate epidemic thresholds, as well as validate theoretical predictions with extensive Monte Carlo simulations. It is shown numerically and theoretically that reducing the social intensity and increasing the number of risk-averse individuals are effective ways of controlling epidemic outbreaks. An appropriate proportion of the risk-averse individual will lead to an epidemic die-out, which is based on a small spreading rate. Our research provides a new perspective for understanding the effect of the population with different social attitudes in the epidemic process.

Bilayer network spreading dynamics driven by community structure and activity

Epidemic outbreaks in the real world are often accompanied by rapid information diffusion, which will change individual behavior patterns and affect the spread of epidemics. The community phenomenon in human society will also have an important influence on the spread of epidemics. The above factors to construct a new bilayer network are considered in this work. The activity-driven model is used to generate time-varying online information contact layer network and offline physical contact layer network. The information diffusion of individual online contact layer is used to affect the epidemic spreading dynamics of offline physical contact layer, and the individual mobility factor is used to control the community structure characteristics. In order to obtain the spreading dynamic equation of the whole network and analyze the spreading threshold of the network effectively, the microscopic Markov chain (MMC) approach is improved and extended to time-varying networks. Experimental verification of Monte Carlo simulations shows that the proposed method is highly accurate in predicting epidemic outbreak thresholds. The results show that individual mobility has no effect on the epidemic outbreak threshold, but it will affect the final number of infections in each community. The greater the individual contact capability of the online contact layer, the smaller the individual contact capability of the offline contact layer that can effectively suppress the epidemic spread. The above findings can present an important reference for effectively preventing and controlling the epidemic transmission in the real world.

The interplay between disease spreading and awareness diffusion in multiplex networks with activity-driven structure.

The interplay between disease and awareness has been extensively studied in static networks. However, most networks in reality will evolve over time. Based on this, we propose a novel epidemiological model in multiplex networks. In this model, the disease spreading layer is a time-varying network generated by the activity-driven model, while the awareness diffusion layer is a static network, and the heterogeneity of individual infection and recovery ability is considered. First, we extend the microscopic Markov chain approach to analytically obtain the epidemic threshold of the model. Then, we simulate the spread of disease and find that stronger heterogeneity in the individual activities of a physical layer can promote disease spreading, while stronger heterogeneity of the virtual layer network will hinder the spread of disease. Interestingly, we find that when the individual infection ability follows Gaussian distribution, the heterogeneity of infection ability has little effect on the spread of disease, but it will significantly affect the epidemic threshold when the individual infection ability follows power-law distribution. Finally, we find the emergence of a metacritical point where the diffusion of awareness is able to control the onset of the epidemics. Our research could cast some light on exploring the dynamics of epidemic spreading in time-varying multiplex networks.

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.

Opinion formation with zealots on temporal network

In decision making, people will integrate various information from complex social environments, however, information flows are constrained by the social network. Past research has demonstrated the structure of social network as well as the existence of zealots can induce some phenomena like information gerrymandering. However, the networks in social context are not static all the time, which raises the question of how opinion forms on the temporal network and how zealots influence the process of opinion formation. In this study, we investigate two scenarios of opinion formation, innovation eruption and election. For the former, we carry out some theoretical analysis based on activity-driven model and find that the existence of zealots will keep the negative opinion, which zealots hold, alive among the population. Then for the election scenario, simulations are performed both on real-world data and synthetic data. We find that the case of temporal network can weaken the effect of the zealots compared with the case of static network, and that the intensity of the effect depends on the connectivity of temporal networks. Comparing with aggregated networks, the temporal network influence the effect of zealots depending on the time interval of the temporal network.

Random walks in time-varying networks with memory.

Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. An individual's memory has been proved to be crucial to affect network evolution and dynamical processes unfolding on the network. In this work, we study the random-walk process on an extended activity-driven network model by taking account of an individual's memory. We analyze how an individual's memory affects random-walk process unfolding on the network when the timescales of the processes of the random walk and the network evolution are comparable. Under the constraints of long-time evolution, we derive analytical solutions for the distribution of walkers at the stationary state and the mean first-passage time of the random-walk process. We find that, compared with the memoryless activity-driven model, an individual's memory enhances the activity fluctuation and leads to the formation of small clusters of mutual contacts with high activity nodes, which reduces a node's capability of gathering walkers, especially for the nodes with large activity, and memory also delays the mean first-passage time. The results on real networks also support the theoretical analysis and numerical results with artificial networks.

Impact of temporal network structures on the speed of consensus formation in opinion dynamics

Opinion dynamics on networks has wide applications to empirical and engineered systems and profound prospects in the general study of complex systems. Many efforts have been devoted to understanding how opinion dynamics is affected by network topology. However, social interactions are best characterized as temporal networks in which ordering of interactions cannot be ignored. Temporal activity patterns including heterogeneous contact strength and interevent times, turnover edge/node dynamics, and daily patterns could have significant effects that would not be captured by static aggregate network representations. In this paper, we study the effects of such temporal patterns on the speed of consensus formation in various models of continuous opinion dynamics using four empirical data sets, including three human face-to-face networks from different real-world settings and a social insect interaction network. We find that static, aggregated networks consistently overestimate the speed of simulated consensus formation while weight heterogeneity associated with frequency of interactions has an inhibitory effect on consensus formation relative to the behavior on unweighted networks. Moreover, the speed of consensus formation is found to be highly sensitive to nodal lifetimes, suggesting that randomization protocols that dramatically alter the distribution of lifetimes cannot be relied upon as reference models. On the other hand, temporal patterns including burstiness of interevent times and the lifetime of edges are found to have insignificant effects on consensus formation. The sensitivity to nodal lifetimes is further demonstrated via synthetic networks generated by an activity-driven model with tunable nodal lifetimes.

Joint effect of individual’s memory and attractiveness in temporal network on spreading dynamics

Most real networks have been found to evolve dynamically. In addition, heterogeneity of interaction strengths and individual’s memory have been proved to be important to affect network evolution in the area of complex networks. Based on a recent extension of the activity-driven modeling framework, i.e. activity-driven model with attractiveness, where individuals are characterized by their activities and attractiveness, we propose a new temporal network model by considering individuals’ memory. Similar to the previous network model, we also investigate heterogeneous distributions and different correlations between the two variables (activity and attractiveness). By numerical simulations, we illustrate the impact of memory on epidemic spreading processes unfolding on the proposed model. We find that, when individuals’ attractiveness is fixed, memory does not cause dramatic change on the epidemic threshold in the SIR process, but it inhibits the epidemic spreading by reducing the infected ratio. While for the SIS process, in the case of uncorrelated and positive correlations between the two variables, memory facilitates the epidemic outbreaks by shrinking the epidemic threshold. When the two variables are negatively correlated, memory does not take obvious impact on the epidemic threshold. Besides, for the two processes unfolding on the network with and without memory, the propagation threshold decreases with the enhancement of the positive correlation, however, it almost does not get much influence from the negative correlation strength. It indicates that for the individuals with same activity, more attractive individuals will promote the disease spread. The findings deepen our understanding of the role of individuals’ memory and their attractiveness in the epidemic spreading process.

Simplicial Activity Driven Model.

Many complex systems find a convenient representation in terms of networks: structures made by pairwise interactions (links) of elements (nodes). For many biological and social systems, elementary interactions involve, however, more than two elements, and simplicial complexes are more adequate to describe such phenomena. Moreover, these interactions often change over time. Here, we propose a framework to model such an evolution: the simplicial activity driven model, in which the building block is a simplex of nodes representing a multiagent interaction. We show analytically and numerically that the use of simplicial structures leads to crucial structural differences with respect to the activity driven model, a paradigmatic temporal network model involving only binary interactions. It also impacts the outcome of paradigmatic processes modeling disease propagation or social contagion. In particular, fluctuations in the number of nodes involved in the interactions can affect the outcome of models of simple contagion processes, contrarily to what happens in the activity driven model.

Random walk on the activity-driven model with mutual selection

Random walks are one of the most fundamental types of stochastic processes and have been applied in various domains, such as ranking systems and searching. In this paper, we investigate random walk process unfolding on a generalized version of the activity-driven modelling framework by considering mutual agreement. The model is characterized by a linking function that describes the probability of the existence of an edge, which depends mutually on the fitness of the vertices on both ends of that edge. We investigate two typical forms of linking functions and derive analytically exact expressions for the asymptotic behavior of random walks and the mean first-passage time for the two cases, respectively. We find that, compared with the activity-driven network model, mutual agreement has nontrivial effects on the properties of random walk processes. For the first case, when the fitness of the ends of a link is independent, we find that the capability of vertices to gather walkers is not only related to the vertices' activity, but also determined by their propensity of receiving connections. For the second case, when the creation of the link is determined by whether the sum of the two end points' fitness is larger than a threshold, we find that for vertices with activity larger than a given threshold, the stronger the activity is, the more walkers they will collect in the stationary state. Finally, we confirm our analytical prediction via large-scale numerical simulations performed by controlling flexible parameters. The results presented here contribute to the understanding of the evolution mechanism of the mutual selection network model and give us an insight into their effects on random walks processes.

AST: Activity-Security-Trust driven modeling of time varying networks

Network modeling is a flexible mathematical structure that enables to identify statistical regularities and structural principles hidden in complex systems. The majority of recent driving forces in modeling complex networks are originated from activity, in which an activity potential of a time invariant function is introduced to identify agents’ interactions and to construct an activity-driven model. However, the new-emerging network evolutions are already deeply coupled with not only the explicit factors (e.g. activity) but also the implicit considerations (e.g. security and trust), so more intrinsic driving forces behind should be integrated into the modeling of time varying networks. The agents undoubtedly seek to build a time-dependent trade-off among activity, security, and trust in generating a new connection to another. Thus, we reasonably propose the Activity-Security-Trust (AST) driven model through synthetically considering the explicit and implicit driving forces (e.g. activity, security, and trust) underlying the decision process. AST-driven model facilitates to more accurately capture highly dynamical network behaviors and figure out the complex evolution process, allowing a profound understanding of the effects of security and trust in driving network evolution, and improving the biases induced by only involving activity representations in analyzing the dynamical processes.

Topological properties of a time-integrated activity-driven network

Here we consider the topological properties of the integrated networks emerging from the activity-driven model [N. Perra et al., Sci. Rep. 2, 469 (2012)], a temporal network model recently proposed to explain the power-law degree distribution empirically observed in many real social networks. By means of a mapping to a hidden-variable network model, we provide analytical expressions for the main topological properties of the integrated network, depending on the integration time and the distribution of activity potential characterizing the model. The expressions obtained, exacts in some cases, the results of controlled asymptotic expansions in others, are confirmed by means of extensive numerical simulations. Our analytical approach, which highlights the differences of the model with respect to the empirical observations made in real social networks, can be easily extended to deal with improved, more realistic modifications of the activity-driven network paradigm.