Dynamical behaviors and spatial diffusion in a psychologically realistic rumor spreading model

2020 ◽  
Vol 31 (02) ◽  
pp. 2050034
Author(s):  
Yingying Cheng ◽  
Liang’an Huo ◽  
Liang Ma ◽  
Hongyuan Guo
Keyword(s):  
Psychological Factors ◽  
Cumulative Effect ◽  
Threshold Condition ◽  
Field Equations ◽  
Final Size ◽  
Dynamical Mechanism ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Mean Field Equations ◽  
Sensory Intensity

The spread of rumors has caused serious social and economic problems, especially during emergencies. Reducing the harm caused by rumors requires understanding the dynamical mechanism by which they propagate. To include the influence of time-dependent psychological factors, this paper proposes an improved rumor spreading model and derives mean-field equations describing the dynamics of rumor spreading. The psychological factors considered are the attenuation of individual interest, the cumulative effect of memory, and changes in sensory intensity with time. We also obtain the threshold condition of rumor spreading. Numerical simulations are used to verify our theoretical results. It is proved that the extremum of the cumulative effect of memory and the rumor attraction rate are positively correlated with the peak number of rumor spreaders, and negatively with the time required to reach the final rumor size. Time grows geometrically, while sensory intensity grows arithmetically. The initial approval rate of the memory accumulation effect and the stifling mechanism have little effect on the final rumor size. Finally, it is found that increasing the attenuation of interest coefficient reduces the time needed for the rumor to reach its final size.

SE2IR Invest Market Rumor Spreading Model Considering Hesitating Mechanism

2019 ◽  
Vol 7 (1) ◽  
pp. 54-69 ◽  
Author(s):  
Hongxing Yao ◽  
Xiangyang Gao
Keyword(s):  
Mean Field ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Field Equations ◽  
Rumor Spreading ◽  
Immunization Strategy ◽  
Scale Free ◽  
Spreading Model ◽  
Mean Field Equations ◽  
The Impact

Abstract According to the actual situation of investor network, a SE2IR rumor spreading model with hesitating mechanism is proposed, and the corresponding mean-field equations is obtained on scale-free network. In this paper, we first combine the theory of spreading dynamics and find out the basic reproductive number R0. And then analyzes the stability of the rumor-free equilibrium and the final rumor size. Finally, we discuss random immune strategies and target immune strategies for the rumor spreading, respectively. Through numerical simulation, we can draw the following conclusions: Reducing the fuzziness and attractiveness of invest market rumor can effectively reduce the impact of rumor. And the target immunization strategy is more effective than the random immunization strategy for the communicators in the invest investor network.

scholarly journals Spreading Dynamics of a 2SIH2R, Rumor Spreading Model in the Homogeneous Network

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yan Wang ◽  
Feng Qing ◽  
Jian-Ping Chai ◽  
Ye-Peng Ni
Keyword(s):  
Cognitive Abilities ◽  
Information Dissemination ◽  
Rapid Development ◽  
Mean Field ◽  
Special Kind ◽  
Field Equations ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Homogeneous Network ◽  
Mean Field Equations

With the rapid development of social network in recent years, the threshold of information dissemination has become lower. Most of the time, rumors, as a special kind of information, are harmful to society. And once the rumor appears, the truth will follow. Considering that the rumor and truth compete with each other like light and darkness in reality, in this paper, we study a rumor spreading model in the homogeneous network called 2SIH2R, in which there are both spreader1 (people who spread the rumor) and spreader2 (people who spread the truth). In this model, we introduced discernible mechanism and confrontation mechanism to quantify the level of people's cognitive abilities and the competition between the rumor and truth. By mean-field equations, steady-state analysis, and numerical simulations in a generated network which is closed and homogeneous, some significant results can be given: the higher the discernible rate of the rumor, the smaller the influence of the rumor; the stronger the confrontation degree of the rumor, the smaller the influence of the rumor; the larger the average degree of the network, the greater the influence of the rumor but the shorter the duration. The model and simulation results provide a quantitative reference for revealing and controlling the spread of the rumor.

Modeling rumor propagation and refutation with time effect in online social networks

2018 ◽  
Vol 29 (08) ◽  
pp. 1850068 ◽  
Author(s):  
Yaming Zhang ◽  
Yanyuan Su ◽  
Weigang Li ◽  
Haiou Liu
Keyword(s):  
Social Networks ◽  
Heterogeneous Networks ◽  
Online Social Networks ◽  
Negative Impact ◽  
Time Effect ◽  
Field Equations ◽  
Two Stage ◽  
Dynamical Mechanism ◽  
Rumor Propagation ◽  
Mean Field Equations

Rumor propagation and refutation form an important issue for spreading dynamics in online social networks (OSNs). In this paper, we introduce a novel two-stage rumor propagation and refutation model with time effect for OSNs. The dynamical mechanism of rumor propagation and refutation with time effect is investigated deeply. Then a two-stage model and the corresponding mean-field equations in both homogeneous and heterogeneous networks are obtained. Monte Carlo simulations are conducted to characterize the dynamics of rumor propagation and refutation in both Watts–Strogatz network and Barabási–Albert network. The results show that heterogeneous networks yield the most effective rumor and anti-rumor spreading. Besides, the sooner authority releases anti-rumor and the more attractive anti-rumor is, the less rumor influence is. What’s more, these findings suggest that individuals’ ability to control themselves and identify rumor accurately should be improved to reduce negative impact of rumor effectively. The results are helpful to understand better the mechanism of rumor propagation and refutation in OSNs.

scholarly journals Optimal Control of Rumor Spreading Model with Consideration of Psychological Factors and Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Liang’an Huo ◽  
Chenyang Ma
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Psychological Factors ◽  
Control Strategies ◽  
Information Age ◽  
Control Cost ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Official Information ◽  
Type Ii Functional Response

Rumors have rapidly increasing influence on the society as well as individual life in the information age. How to control the spread of such rumors effectively has become an urgent problem to be solved. In this paper, we consider an optimal control of rumor spreading model with psychological factors and time delay. Firstly, we introduce a realistic optimal control of rumor spreading model with consideration of Holling-type II functional response and time delay. Secondly, by introducing two control strategies of both promoting scientific knowledge and releasing official information, we formulate an optimal control problem to minimize both the number of ignorant individuals and spreaders and the control cost. Thirdly, we prove the existence and the necessary conditions of optimal control strategies theoretically based on Pontryagin’s maximum principle. Our results indicate that the proposed control strategies are effective in reducing the number of spreaders and ignorant individuals and minimizing control cost.

scholarly journals Dynamical Analysis of Rumor Spreading Model considering Node Activity in Complex Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Liang’an Huo ◽  
Fan Ding ◽  
Chen Liu ◽  
Yingying Cheng
Keyword(s):  
Complex Networks ◽  
Dynamic Models ◽  
Spreading Rate ◽  
Dynamical Analysis ◽  
Field Equations ◽  
Spreading Process ◽  
Rumor Spreading ◽  
Node Activity ◽  
Activity Rate ◽  
Mean Field Equations

The dynamic models are proposed to investigate the influence node activity has on rumor spreading process in both homogeneous and heterogeneous networks. Different from previous studies, we believe that the activity of nodes in complex networks affects the process of rumor spreading. An active node can have contact with all the nodes it directly links to, while an inactive node could only interact with its active neighbors. We explore the joint effort of activity rate, spreading rate and network topology on rumor spreading process by mean-field equations and numerical simulations, which reveals that there exists a critical curve consisting of critical activity rate and spreading rate; meanwhile, activity rate and spreading rate both have influence on the final rumor spreading scale.

The influence of oblivion-recall mechanism and loss-interest mechanism on the spread of rumors in complex networks

2019 ◽  
Vol 30 (09) ◽  
pp. 1950075 ◽  
Author(s):  
Wang Jing ◽  
Li Min ◽  
Wang Ya-Qi ◽  
Zhou Zi-Chen ◽  
Zhang Li-Qiong
Keyword(s):  
Mean Field ◽  
Stable State ◽  
Sir Model ◽  
Field Equations ◽  
Independent State ◽  
Rumor Spreading ◽  
Mean Field Equations ◽  
Angle Of View ◽  
Two Parameters ◽  
The Impact

Studying more realistic propagation mechanisms of rumors is crucial to controlling their spreading. Considering the reality of people’s forgetting and losing interest in the process of rumor spreading, the oblivion-recall mechanism and the loss-interest mechanism are both introduced in this paper to construct a novel susceptible-infected-removed (SIR) model. In our SIR model, the forgetting is regarded as an independent state type of the population, and we use the forgetting factor [Formula: see text] and the recall factor [Formula: see text] to characterize the oblivion-recall mechanism. The mean-field equations are established respectively to describe the transmission dynamics of rumors in homogeneous networks and inhomogeneous networks. By performing stable state analysis, the relationship between these two parameters [Formula: see text], [Formula: see text] and the propagation critical thresholds [Formula: see text] is investigated. It shows that [Formula: see text] is directly proportional to [Formula: see text], which indicates that the loss-interest mechanism makes [Formula: see text] exist, and the oblivion-recall mechanism increases the value of [Formula: see text]. Thus, the oblivion-recall mechanism reduces the outbreak probability of rumor spreading. It also reveals that when considering the impact of oblivion-recall mechanism, both the final rumor size and the propagation velocity of rumors decrease. Moreover, in the case of considering the existence of oblivion-recall mechanism, it is still found that the network topology is an important factor affecting the spread of rumors. We wish that our study can offer a new angle of view on the issue of the spread of rumors.

scholarly journals A Rumor Spreading Model considering the Cumulative Effects of Memory

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Yi Zhang ◽  
Jiuping Xu
Keyword(s):  
Numerical Solutions ◽  
Memory Effects ◽  
Average Degree ◽  
Cumulative Effects ◽  
Final Size ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Constant Rate ◽  
Artificial Network ◽  
Changes Over Time

This paper proposes a rumor spreading model which examines how the memory effects rate changes over time in artificial network and a real social network. This model emphasizes a special rumor spreading characteristic called “the cumulative effects of memory.” A functionp(t)reflecting the cumulative memory effects is established, which replaces the constant rate of memory effects in the traditional model. Further, rumor spreading model simulations are conducted with different parameters in three artificial networks. The results show that all the parameters but the initial memory rate of memory effects function have a significant impact on rumor spreading. At the same time, the simulation results show that the final size of the stiflers is sensitive to the average degreekwhen it is small but is not sensitive tokwhen the average degree is greater than a certain degree. Finally, through investigations on the Sina Microblog network, the numerical solutions show that the peak value and final size of the rumor spreading are much larger under a variable memory effects rate than under a constant rate.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals Dynamical analysis of a stochastic rumor-spreading model with Holling II functional response function and time delay

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liang’an Huo ◽  
Xiaomin Chen
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Functional Response ◽  
Response Function ◽  
Rapid Development ◽  
Dynamical Behavior ◽  
Deterministic System ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Holling Ii Functional Response

AbstractWith 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.

Precipitation in small systems—II. Mean field equations more effective than population balance

1996 ◽  
Vol 51 (19) ◽  
pp. 4423-4436 ◽  
Author(s):  
S. Manjunath ◽  
K.S. Gandhi ◽  
R. Kumar ◽  
Doraiswami Ramkrishna
Keyword(s):  
Mean Field ◽  
Population Balance ◽  
Field Equations ◽  
Small Systems ◽  
Mean Field Equations
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