We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behavior and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.
We introduce here a multi-type bootstrap percolation model, which we call T-Bootstrap Percolation (T-BP), and apply it to study information propagation in social networks. In this model, a social network is represented by a graph G whose vertices have different labels corresponding to the type of role the person plays in the network (e.g. a student, an educator, etc.). Once an initial set of vertices of G is randomly selected to be carrying a gossip (e.g. to be infected), the gossip propagates to a new vertex provided it is transmitted by a minimum threshold of vertices with different labels. …
For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of describing these effects. We present an extended model for disease spread based on combining an SIR model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. The model shows interesting nonequilibrium phase separation associated with a reduction of the number of infections, and …
We have two main aims in this paper. First we use theories of disease spreading on networks to look at the COVID-19 epidemic on the basis of individual contacts -- these give rise to predictions which are often rather different from the homogeneous mixing approaches usually used. Our second aim is to look at the role of social deprivation, again using networks as our basis, in the spread of this epidemic. We choose the city of Kolkata as a case study, but assert that the insights so obtained are applicable to a wide variety of urban environments which are densely populated and where social ine…
Information spreading has been studied for decades, but its underlying mechanism is still under debate, especially for those ones spreading extremely fast through Internet. By focusing on the information spreading data of six typical events on Sina Weibo, we surprisingly find that the spreading of modern information shows some new features, i.e. either extremely fast or slow, depending on the individual events. To understand its mechanism, we present a Susceptible-Accepted-Recovered (SAR) model with both information sensitivity and social reinforcement. Numerical simulations show that the mode…
Influence overlap is a universal phenomenon in influence spreading for social networks. In this paper, we argue that the redundant influence generated by influence overlap cause negative effect for maximizing spreading influence. Firstly, we present a theoretical method to calculate the influence overlap and record the redundant influence. Then in term of eliminating redundant influence, we present two algorithms, namely, Degree-Redundant-Influence (DRS) and Degree-Second-Neighborhood (DSN) for multiple spreaders identification. The experiments for four empirical social networks successfully v…
Large-scale rumor spreading could pose severe social and economic damages. The emergence of online social networks along with the new media can even make rumor spreading more severe. Effective control of rumor spreading is of theoretical and practical significance. This paper takes the first step to understand how the blockchain technology can help limit the spread of rumors. Specifically, we develop a new paradigm for social networks embedded with the blockchain technology, which employs decentralized contracts to motivate trust networks as well as secure information exchange contract. We des…
Non-pharmaceutical measures such as social distancing, can play an important role to control an epidemic in the absence of vaccinations. In this paper, we study the impact of social distancing on epidemics for which it is executable. We use a mathematical model combining human mobility and disease spreading. For the mobility dynamics, we design an agent based model consisting of pedestrian dynamics with a novel type of force to resemble social distancing in crowded sites. For the spreading dynamics, we consider the compartmental SIE dynamics plus an indirect transmission with the footprints of…
The goal of opinion maximization is to maximize the positive view towards a product, an ideology or any entity among the individuals in social networks. So far, opinion maximization is mainly studied as finding a set of influential nodes for fast content dissemination in a social network. In this paper, we propose a novel approach to solve the problem, where opinion maximization is achieved through efficient information spreading. In our model, multiple sources inject information continuously into the network, while the regular nodes with heterogeneous social learning abilities spread the info…
In this final chapter, we consider the state-of-the-art for spreading in social systems and discuss the future of the field. As part of this reflection, we identify a set of key challenges ahead. The challenges include the following questions: how can we improve the quality, quantity, extent, and accessibility of datasets? How can we extract more information from limited datasets? How can we take individual cognition and decision making processes into account? How can we incorporate other complexity of the real contagion processes? Finally, how can we translate research into positive real-worl…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected individuals. For a given social distancing individual strategies, we establish the epidemic reproduction number $R_0$ which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper we study the equilibrium of the social distancing game, in which individuals choose their social distancing level according to an a…
The aim of this paper consists in the application of a recent epidemiological model, namely SEIR with Social Distancing (SEIR--SD), extended here through the definition of a social distancing function varying over time, to assess the situation related to the spreading of the coronavirus Covid--19 in Italy and in two of its most important regions, i.e., Lombardy and Campania. To profitably use this model, the most suitable values of its parameters must be found. The estimation of the SEIR--SD model parameters takes place here through the use of Differential Evolution, a heuristic optimization t…
In this work, we address a multicoupled dynamics on complex networks with tunable structural segregation. Specifically, we work on a networked epidemic spreading under a vaccination campaign with agents in favor and against the vaccine. Our results show that such coupled dynamics exhibits a myriad of phenomena such as nonequilibrium transitions accompanied by bistability. Besides we observe the emergence of an intermediate optimal segregation level where the community structure enhances negative opinions over vaccination but counterintuitively hinders - rather than favoring - the global diseas…
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 d…
Peer influence and social contagion are key denominators in the adoption and participation of information spreading, such as news propagation, word-of-mouth or viral marketing. In this study, we argue that it is biased to only focus on the scale and coverage of information spreading, and propose that the level of influence reinforcement, quantified by the re-exposure rate, i.e., the rate of individuals who are repeatedly exposed to the same information, should be considered together to measure the effectiveness of spreading. We show that local network structural characteristics significantly a…
To date, the only effective means to respond to the spreading of COVID-19 pandemic are non-pharmaceutical interventions (NPIs), which entail policies to reduce social activity and mobility restrictions. Quantifying their effect is difficult, but it is key to reduce their social and economical consequences. Here, we introduce a meta-population model based on temporal networks, calibrated on the COVID-19 outbreak data in Italy and apt to evaluate the outcomes of these two types of NPIs. Our approach combines the advantages of granular spatial modelling of meta-population models with the ability …
To contain the propagation of emerging diseases that are transmissible from human to human, non-pharmaceutical interventions (NPIs) aimed at reducing the interactions between humans are usually implemented. One example of the latter kind of measures is social distancing, which can be either policy-driven or can arise endogenously in the population as a consequence of the fear of infection. However, if NPIs are lifted before the population reaches herd immunity, further re-introductions of the pathogen would lead to secondary infections. Here we study the effects of different social distancing …
We investigate the problem of locating the source of a self-interacting signal spreading in a complex networks. We use a well-known rumour model as an example of the process with self-interaction. According to this model based on the SIR epidemic dynamics, the infected nodes may interact and discourage each other from gossiping with probability $α$. We compare three algorithms of source localization: Limited Pinto-Thiran-Vettarli (LPTV), Gradient Maximum Likelihood (GMLA) and one based on Pearson correlation between time and distance. The results of numerical simulations show that additional i…
Social networks are the prime channel for the spreading of computer viruses. Yet the study of their propagation neglects the temporal nature of social interactions and the heterogeneity of users' susceptibility. Here, we introduce a theoretical framework that captures both properties. We study two realistic types of viruses propagating on temporal networks featuring Q categories of susceptibility and derive analytically the invasion threshold. We found that the temporal coupling of categories might increase the fragility of the system to cyber threats. Our results show that networks' dynamics …
Agent-based simulations of emotion spreading in online social networks
对来自在线社交网络的经验数据的定量分析揭示了情感参与的群体动态（Šuvakov et al）。然而，充分了解其内在机制仍然是一项具有挑战性的任务。利用基于Agent的计算机模拟，本文研究了在线社交网络中情感交流的动力学。从\texttt{MySpace}社会网络的经验数据集出发，得到了指导主体如何交互的规则，并推导出了现实的网络结构和一些重要的参数。Agent的情绪状态由两个变量表征，一个是对刺激的反应性，另一个是吸引力或厌恶度，通过这两个变量可以定义常见的情绪。代理人的行动是由增强的唤醒触发的。高分辨率的动态实现，其中每个消息携带代理的情绪沿网络链路被确定，其对接收代理的影响被认为是不断老化的时间。我们的研究结果表明：（i）聚合的群体行为可能产生于个体的情感行为;（ii）集体状态的特点是时间的相关性和占主导地位的积极情绪出现，类似于经验系统;（iii）驱动信号的性质--用户进入网络世界的速度，对建立连贯的行为有深远的影响，这是观察到的用户在在线社交网络。此外，我们的模拟表明，情绪的传播模式不同，例如，“热情”和“惭愧”，这两个词的情感内涵完全不同。{ \bf {本研究中使用的所有数据均完全匿名。}}
