Stability analysis and optimal control of a rumor spreading model with media report

2019 ◽  
Vol 517 ◽  
pp. 551-562 ◽  
Author(s):  
Liang’an Huo ◽  
Li Wang ◽  
Xiaomin Zhao
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Media Report ◽  
Rumor Spreading ◽  
Spreading Model

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 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.

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