scholarly journals Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Zhongxue Chang ◽  
Haijun Jiang ◽  
Shuzhen Yu ◽  
Shanshan Chen
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Complex Networks ◽  
Minimum Principle ◽  
Mean Field Theory ◽  
Mean Field ◽  
Propagation Model ◽  
Nonlinear Incidence ◽  
Rumor Propagation ◽  
Spreading Dynamics

An Innocents-Spreaders-Calmness-Removes (ISCR) rumor propagation model is established with nonlinear incidence and time delay on complex networks in this paper. Based on the mean-field theory, the spreading dynamics of the ISCR model are discussed in detail. Firstly, the basic reproduction number R 0 is obtained by the next generation matrix method to ensure the existence of rumor-prevailing equilibrium. Secondly, by utilizing the Routh–Hurwitz criterion and LaSalle’s invariance principle, the local stability and global stability of rumor equilibria are proved. Moreover, the optimal control is presented via Pontryagin’s minimum principle, which is to effectively restrain rumor diffusion. Finally, the theoretical results are verified by numerical simulations.

Optimal control of a rumor model with group propagation over complex networks

2020 ◽  
pp. 2150035
Author(s):  
Kalaiselvi Myilsamy ◽  
Muthukrishnan Senthil Kumar ◽  
Athira Satheesh Kumar
Keyword(s):  
Optimal Control ◽  
Mobile Networks ◽  
Social Life ◽  
Minimum Principle ◽  
Mean Field Theory ◽  
Mean Field ◽  
Real Life ◽  
Heterogeneous Model ◽  
The People ◽  
Spreading Dynamics

Rumor is an unauthenticated statement that gives significant changes in the social life of the people, financial markets (stocks and trades), etc. By incorporating the dissemination of rumor through groups in social, mobile networks and by considering the people’s cognitive factor (hesitate and forget), a new model on the rumor spreading process is presented in this paper. The spreading dynamics of rumor in homogeneous and heterogeneous networks is analyzed by using mean-field theory. The reproduction number is obtained by using the next-generation matrix. The global stability of the rumor-free equilibrium for the homogeneous and heterogeneous model is proved elaborately. An optimal control problem is developed to minimize the hesitators and infected persons and the existence of optimality is shown using Pontryagin’s Minimum Principle. The hesitating and forgetting mechanism has a great impact on the model and is similar to the real-life. Further, the control parameters work superior in controlling the spreading of rumors. Finally, the numerical results are verified by the analytical results.

Rumor Propagation Model for Complex Network with Non-Uniform Propagation Rates

2014 ◽  
Vol 596 ◽  
pp. 868-872 ◽  
Author(s):  
Rui Sun ◽  
Wan Bo Luo
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Propagation Rate ◽  
Propagation Model ◽  
Scale Free Network ◽  
Propagation Characteristics ◽  
Affecting Factors ◽  
Scale Free ◽  
Rumor Propagation ◽  
Free Network

Considering propagation characteristics and affecting factors of rumor in real-world complex networks, this paper described different propagation rates of different nodes by introducing the rumor acceptability function. Based on mean-field theory, this paper presented a rumor propagation model with non-uniform propagation rate, and then simulated the behaviour of rumor propagation on scale-free network and calculated the propagation thresholds by corresponding dynamics equation. Theoretical analysis and simulation results show that nodes with different rumor acceptability could lead to slowing the spread of rumors, make positive propagation threshold arise, and effectively contain the outbreak and reduce the risk of rumors.

Spreading of Epidemics on Scale-Free Networks with Time Delay

2012 ◽  
Vol 562-564 ◽  
pp. 1386-1389
Author(s):  
Yuan Mei Wang ◽  
Tao Li
Keyword(s):  
Field Theory ◽  
Time Delay ◽  
Mean Field Theory ◽  
Mean Field ◽  
Sir Model ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
Theoretical Results

In the SIR model once a node is cured after infection it becomes permanently immune,but we assume this immunity to be temporary. So we obtain an epidemic model with time delay on scale-free networks. Using the mean field theory the spreading threshold and the spreading dynamics is analyzed. Theoretical results indicate that the threshold is significantly dependent on the topology of scale-free networks and time delay. Numerical simulations confirmed the theoretical results.

scholarly journals Optimal Control of ISTR Rumor Propagation Model with Social Reinforcement in Heterogeneous Network

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Liang’an Huo ◽  
Sijing Chen ◽  
Xiaoxiao Xie ◽  
Huiyuan Liu ◽  
Jianjia He
Keyword(s):  
Optimal Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Principle ◽  
Optimal Solution ◽  
Propagation Model ◽  
Social Reinforcement ◽  
Social Stability ◽  
Rumor Propagation ◽  
Rumor Control

The wide spread of rumor is undoubtedly harmful to social stability; we should try to lower the effect of rumor on society. Therefore, it is reasonable to put forward the rumor control strategy on the basis of the study of the law of rumor propagation. Firstly, the ISTR model of rumor is established by including influencing factors of true information spreader and social reinforcement. And by using the next generation matrix method, the basic reproduction number of rumor is obtained. Then, in order to minimize the adverse effects of rumors, through introducing two control strategies of scientific knowledge popularization and refutation of rumors, the optimal control problem is established. And through using Pontryagin’s Minimum Principle, the optimal solution of the rumor propagation model is solved. Finally, through theoretical analysis and numerical simulation, some results can be obtained. The results show that adding true information spreaders into the rumor model can effectively control the rumor propagation, and social reinforcement plays a significance role in rumor. The results also prove that these two control strategies can effectively inhibit the propagation of rumors. With the addition of control strategies, the number of true information spreaders increases, while the number of rumor spreaders decreases.

Research on SIQRS Spreading Dynamic Model with Feedback Mechanism on Scale-Free Networks

2014 ◽  
Vol 989-994 ◽  
pp. 4524-4527
Author(s):  
Tao Li ◽  
Yuan Mei Wang ◽  
You Ping Yang
Keyword(s):  
Dynamic Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Feedback Mechanism ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
The Relationship

A modified spreading dynamic model with feedback-mechanism based on scale-free networks is presented in this study. Using the mean field theory, the spreading dynamics of the model is analyzed. The spreading threshold and equilibriums are derived. The relationship between the spreading threshold, the epidemic steady-state and the feedback-mechanism is analyzed in detail. Theoretical results indicate the feedback-mechanism can increase the spreading threshold, resulting in effectively controlling the epidemic spreading.

SIR rumor spreading model considering the effect of difference in nodes’ identification capabilities

2017 ◽  
Vol 28 (05) ◽  
pp. 1750060 ◽  
Author(s):  
Ya-Qi Wang ◽  
Jing Wang
Keyword(s):  
Transmission Rate ◽  
Mean Field Theory ◽  
Mean Field ◽  
Rumor Spreading ◽  
Network Nodes ◽  
Critical Thresholds ◽  
Rumor Propagation ◽  
Dynamical Behaviors ◽  
The Mean ◽  
The Difference

In this paper, we study the effect of difference in network nodes’ identification capabilities on rumor propagation. A novel susceptible-infected-removed (SIR) model is proposed, based on the mean-field theory, to investigate the dynamical behaviors of such model on homogeneous networks and inhomogeneous networks, respectively. Theoretical analysis and simulation results demonstrate that when we consider the influence of difference in nodes’ identification capabilities, the critical thresholds obviously increase, but the final rumor sizes are apparently reduced. We also find that the difference in nodes’ identification capabilities prolongs the time of rumor propagation reaching a steady state, and decreases the number of nodes that finally accept rumors. Additionally, under the influence of difference of nodes’ identification capabilities, compared with the homogeneous networks, the rumor transmission rate on the inhomogeneous networks is relatively large.

scholarly journals Mean-field theory of superradiant phase transition in complex networks

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Andrei Yu. Bazhenov ◽  
Dmitriy V. Tsarev ◽  
Alexander P. Alodjants
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Complex Networks ◽  
Mean Field Theory ◽  
Mean Field ◽  
Superradiant Phase
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