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In this paper, we studied a delayed rumor spreading model with discontinuous threshold control. First, we studied the existence of equilibria of the subsystem. Regarding the delay as bifurcating parameter, the local asymptotic stability and Hopf bifurcation of the positive equilibrium are discussed by analyzing the corresponding characteristic equations of linearized systems. Then, we studied the existence of the sliding mode and analyzed the existence of the tangent equilibria, boundary equilibria, regular equilibria, and the stability of the pseudo-equilibrium. Finally, we provide some numerical simulations to verify the theoretical results.

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Objective: To explore the law of opinion dissemination and individual opinion evolution at the micro level, this paper analyzes the influence of variation and oyster on communication from the perspective of network structure. Methods: In this paper, we introduce the concepts of "variation" and "oyster", build a multi-layer coupled network environment combined with the ISOVR model, and conduct simulation experiments of network information dissemination based on the bounded trust model. Results: The experimental results reveal that the extent and scope of variation's spread in the network are more dependent on the trust of nodes themselves, and decreasing the trust of nodes significantly reduces the rate and peak value of variation. Changing the silence coefficient of variation does not effectively change the direction of rumor propagation, which indicates that rumor has a strong propagation ability after mutation. Conclusion: The insights of this paper on the dissemination of public opinions include: 1) pay attention to people with high trust levels, such as opinion leaders; 2) clarify the misinformation in time to prevent further spread of rumors.

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Since the outbreak of COVID-19, many studies have explored the influencing factors of rumor spreading, such as anxiety, risk perception and information source credibility, but few studies have focused on the impact of individual differences. Based on the theory of behavioral immune systems, we investigated the impact of perceived infectability on rumor spreading and the mediating role of rumor trust in the context of COVID-19. Two studies were investigated using the scale and recall-report task of rumor spreading. The results show that perceived infectability was a significant positive predictor of rumor spreading. However, the impact of perceived infectability on rumor spreading was not direct, and it mainly indirectly affected rumor spreading through the mediating role of rumor trust. Overall, the findings suggest that individuals with high perceived infectability are more likely to believe rumors and then spread rumors during the epidemic. This study advances the literature on rumor spreading and behavioral immune systems and provides practical implications to anti-rumor campaigns.

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In the current era, information dissemination is more convenient, the harm of rumors is more serious than ever. At the beginning of 2020, COVID-19 is a biochemical weapon made by a laboratory, which has caused a very bad impact on the world. It is very important to control the spread of these untrue statements to reduce their impact on people's lives. In this paper, a new rumor spreading model with comprehensive interventions (background detection, public education, official debunking, legal punishment) is proposed for qualitative and quantitative analysis. The basic reproduction number with important biological significance is calculated, and the stability of equilibria is proved. Through the optimal control theory, the expression of optimal control pairs is obtained. In the following numerical simulation, the optimal control under 11 control strategies are simulated. Through the data analysis of incremental cost-effectiveness ratio and infection averted ratio of all control strategies, if we consider the control problem from different perspectives, we will get different optimal control strategies. Our results provide a flexible control strategy for the security management department.

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In this paper, we propose and analyze from a stability viewpoint a deterministic, ODE-based class of rumor spreading models with two distinct inhibiting and adjusting mechanisms, together with its corresponding stochastic counterpart. For the deterministic model, a threshold parameter R 0 defined ad hoc, called the basic influence number, is used to ascertain whether the rumors are prevailing or not. If R 0 < 1 , the rumor-free equilibrium is found to be locally asymptotically stable, while if R 0 > 1 it is shown that there is at least one additional rumor-prevailing equilibrium, which is necessarily locally asymptotically stable. For the stochastic model, we first show that there exists a unique global solution. Subsequently, we investigate the asymptotic behavior of the stochastic system around the equilibria of the deterministic system by constructing suitable Lyapunov functionals. Furthermore, numerical simulations are given to illustrate, support and enhance our theoretical analysis.

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Inspired by the Daley-Kendall and Goffman-Newill models, we propose an Ignorant-Believer-Unbeliever rumor (or fake news) spreading model with the following characteristics: (i) a network contact between individuals that determines the spread of rumors; (ii) the value (cost versus benefit) for individuals who search for truthful information (learning); (iii) an impact measure that assesses the risk of believing the rumor; (iv) an individual search strategy based on the probability that an individual searches for truthful information; (v) the population search strategy based on the proportion of individuals of the population who decide to search for truthful information; (vi) a payoff for the individuals that depends on the parameters of the model and the strategies of the individuals. Furthermore, we introduce evolutionary information search dynamics and study the dynamics of population search strategies. For each value of searching for information, we compute evolutionarily stable information (ESI) search strategies (occurring in non-cooperative environments), which are the attractors of the information search dynamics, and the optimal information (OI) search strategy (occurring in (eventually forced) cooperative environments) that maximizes the expected information payoff for the population. For rumors that are advantageous or harmful to the population (positive or negative impact), we show the existence of distinct scenarios that depend on the value of searching for truthful information. We fully discuss which evolutionarily stable information (ESI) search strategies and which optimal information (OI) search strategies eradicate (or not) the rumor and the corresponding expected payoffs. As a corollary of our results, a recommendation for legislators and policymakers who aim to eradicate harmful rumors is to make the search for truthful information free or rewarding.

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With the rapid development of information society, rumor plays an increasingly crucial part in social communication, and its spreading has a significant impact on human life. In this paper, a stochastic rumor-spreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise is proposed. Firstly, the existence of a unique global positive solution of the model is studied. Then the asymptotic behavior of the global solution around the rumor-free and rumor-local equilibrium nodes of the deterministic system is discussed. Finally, through some numerical results, the validity and availability of theoretical analysis is verified powerfully, and it shows that some factors such as the transmission rate, the intensity of white noise, and the time delay have significant relationship with the dynamical behavior of rumor spreading.

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The research on rumor spreading has a long history, and its wanton flooding has brought huge impact on people's life. In the process of its spreading, the individual's activity plays an important role. However, in the complex and changeable environment, randomness cannot be ignored, not to mention its influence on individual activity Based on the I S R model of individual activity, this paper explores the stochastic version of the rumor model including fluctuations in the activity. Then, the influence of Stratonovich stochastic noise on the asymptotic behavior of non-linear rumor spreading model is studied. Through the mathematical analysis, we get the critical values to measure whether the deterministic and stochastics models spread or not, as well as the threshold conditions for rumor to spread wantonly. At the same time, the effects of Stratonovich stochastic noise on the asymptotic behavior of rumor-free equilibrium point E 0 and endemic equilibrium point E ∗ are obtained respectively, and the condition that the rumor-free equilibrium is globally asymptotically stable in the presence of noise is given. Finally, the theoretical results are verified by numerical simulation.

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This paper studies the rumor propagation model with heterogeneous networks in a multilingual environment. Firstly, a rumor propagation model with two language spreaders, in which the immunologic mechanism is considered in the ignorant, is proposed on heterogeneous networks. Secondly, the basic reproduction number and the dynamic behaviors are analyzed by using the next-generation matrix method and Lyapunov stability theory, respectively. Moreover, two control strategies are designed to effectively suppress the spread of the rumor. The one is continuous control strategy. By applying real-time control to the spreaders, the rumor spreading time can be greatly reduced and the rumor can die out in a short time. The other is event-triggered impulsive control strategy, which can effectively reduce the consumption of resources and ensure the extinction of the rumor. Finally, the correctness of theoretical analysis and the feasibility of control methods are verified by numerical simulations.

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The wide availability of user-provided content in online social media facilitates the aggregation of people around common interests, worldviews, and narratives. However, the World Wide Web (WWW) also allows for the rapid dissemination of unsubstantiated rumors and conspiracy theories that often elicit rapid, large, but naive social responses such as the recent case of Jade Helm 15--where a simple military exercise turned out to be perceived as the beginning of a new civil war in the United States. In this work, we address the determinants governing misinformation spreading through a thorough quantitative analysis. In particular, we focus on how Facebook users consume information related to two distinct narratives: scientific and conspiracy news. We find that, although consumers of scientific and conspiracy stories present similar consumption patterns with respect to content, cascade dynamics differ. Selective exposure to content is the primary driver of content diffusion and generates the formation of homogeneous clusters, i.e., "echo chambers." Indeed, homogeneity appears to be the primary driver for the diffusion of contents and each echo chamber has its own cascade dynamics. Finally, we introduce a data-driven percolation model mimicking rumor spreading and we show that homogeneity and polarization are the main determinants for predicting cascades' size.

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