scholarly journals Spread Mechanism and Control Strategies of Rumor Propagation Model Considering Rumor Refutation and Information Feedback in Emergency Management

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1694
Author(s):  
Jianhong Chen ◽  
Chaoqun Chen ◽  
Qinghua Song ◽  
Yifei Zhao ◽  
Longxin Deng ◽  
...  
Keyword(s):  
Equilibrium State ◽  
Emergency Management ◽  
Equilibrium Point ◽  
Open System ◽  
Endemic Equilibrium ◽  
Propagation Model ◽  
Information Feedback ◽  
Rumor Spreading ◽  
Rumor Propagation ◽  
Management Procedures

The rumor-free equilibrium state and rumor-endemic equilibrium state are two symmetric descriptions of the status of a system. The constant spreading of rumors would affect the smooth operation of emergency management procedures and cause unnecessary social and economic loss. To reduce the negative effect of rumor propagation, in this paper, we introduce a compartmental model of rumor propagation, which considers the rumor refutation of public and information feedback. By deriving mean-field equations that describe the dynamics of the model, we use analytical and numerical solutions of these equations to investigate the threshold and dynamics of the model in both the closed system and open system. The results imply that the initial equilibrium point is not stable and there exists a rumor-free equilibrium point; in the open system, there exists a threshold beyond which rumors can spread; the stability of the initial equilibrium point is related to the threshold R0 = (φ*α)/μ, and there exists a rumor-endemic equilibrium point. The development process of rumor propagation can be divided into four stages: latent period, progressive period, intense period, and recession period. Under the influence of population, rumor spreading can exceed the threshold readily because the migration rate μ is usually less than the proportion of ignorants without critical ability φ, and the rumor spreading process in an open system presents a fluctuating development, the rumor would not disappear in this autonomous system. Based on the analysis, we propose some measures, such as providing open and efficient information queries and exchange platforms, etc.

Dynamic Analysis of a Reaction–Diffusion Rumor Propagation Model

2016 ◽  
Vol 26 (06) ◽  
pp. 1650101 ◽  
Author(s):  
Hongyong Zhao ◽  
Linhe Zhu
Keyword(s):  
Social Networks ◽  
Time Delay ◽  
New Media ◽  
Equilibrium Point ◽  
Rapid Development ◽  
Upper And Lower Solutions ◽  
Propagation Model ◽  
Traveling Wave Solution ◽  
Rumor Spreading ◽  
Rumor Propagation

The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.

scholarly journals Dynamics Analysis of a Delayed Rumor Propagation Model in an Emergency-Affected Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Chunru Li ◽  
Zujun Ma
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Propagation Model ◽  
Positive Equilibrium ◽  
Center Manifold Theorem ◽  
Rumor Propagation ◽  
Boundary Equilibrium ◽  
Normal Form Method ◽  
Positive Equilibrium Point ◽  
The Stability

Rumors influence people’s decisions in an emergency-affected environment. How to describe the spreading mechanism is significant. In this paper, we propose a delayed rumor propagation model in emergencies. By taking the delay as the bifurcation parameter, the local stability of the boundary equilibrium point and the positive equilibrium point is investigated and the conditions of Hopf bifurcation are obtained. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, some numerical simulations are also given to illustrate our theoretical results.

Mathematical analysis of information propagation model in complex networks

2020 ◽  
Vol 34 (26) ◽  
pp. 2050240
Author(s):  
Linhe Zhu ◽  
Gui Guan ◽  
Zhengdi Zhang
Keyword(s):  
Time Delay ◽  
Online Social Networks ◽  
Nonnegative Solution ◽  
Equilibrium Points ◽  
Propagation Model ◽  
Spatial Distance ◽  
Positive Equilibrium ◽  
Rumor Spreading ◽  
Unique Existence ◽  
Rumor Propagation

In virtue of identifying the influence of nodes, the spatial distance of rumor propagation is defined with the partition and clustering in the network. Considering the temporal and spatial propagation characteristics of rumors in online social networks, we establish a delayed rumor propagation model based on the graph theory and partial functional differential equations. Firstly, the unique existence and uniform boundedness of the nonnegative solution are explored. Secondly, we discuss the existence of positive equilibrium points sufficiently. Thirdly, stabilities of the rumor-free and rumor-spreading equilibrium points are investigated according to the linearization approach and Lyapunov function. Finally, we perform several numerical simulations to validate theoretical results and show the influence of time delay on rumor propagation. Experimental results further illustrate that taking forceful actions such as increasing the time delay in the rumor-spreading process can control rumor propagation due to the timely effectiveness of the information.

scholarly journals Rumor Propagation Model: An Equilibrium Study

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
José Roberto C. Piqueira
Keyword(s):  
Initial Conditions ◽  
Equilibrium Points ◽  
Propagation Model ◽  
Epidemiological Models ◽  
Rumor Spreading ◽  
Equilibrium Study ◽  
Spreading Model ◽  
Rumor Propagation ◽  
Propagation Parameters ◽  
The 1960S

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

A Rumor & Anti-rumor Propagation Model Based on Data Enhancement and Evolutionary Game

2020 ◽  
pp. 1-1
Author(s):  
Yunpeng Xiao ◽  
Wen Li ◽  
Shuai Qiang ◽  
Qian Li ◽  
Hanchun Xiao ◽  
...  
Keyword(s):  
Evolutionary Game ◽  
Propagation Model ◽  
Model Based ◽  
Rumor Propagation

MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
The Mathematical Model ◽  
Globally Stable ◽  
Well Posed ◽  
The Basic Reproduction Number ◽  
Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

scholarly journals Analisis Kestabilan Model Matematika Ko-infeksi Virus Influenza A dan Pneumokokus pada Sel Inang

2020 ◽  
Vol 1 (2) ◽  
pp. 74
Author(s):  
Abdul Faliq Anwar ◽  
Windarto Windarto ◽  
Cicik Alfiniyah
Keyword(s):  
Equilibrium Point ◽  
Influenza A Virus ◽  
Basic Reproduction Number ◽  
Influenza A ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Infected Host Cell ◽  
Stability Of Equilibrium ◽  
Next Generation Matrix ◽  
Virus Influenza

Co-infection of influenza A virus and pneumococcus is caused by influenza A virus and pneumococcus bacteria which infected host cell at the same time. The purpose of this thesis is to analyze stability of equilibrium point on mathematical model within-host co-infection of influenza A and pneumococcus. Based on anlytical result of the model there are four quilibrium points, non endemic co-infection equilibrium (E0), endemic influenza A virus equilibrium (E1), endemic pneumococcus equilbrium (E2) and endemic co-infection equilibrium (E3). By Next Generation Matrix (NGM), we obtain two basic reproduction number, which are basic reproduction number for influenza A virus (R0v) and basic reproduction number for pneumococcus (R0b). Existence of equilibrium point and local stability of equilibrium point dependent on basic reproduction number. Non endemic co-infection equilibrium is locally asymtotically stable if R0v < 1 and R0b < 1; influenza A virus endemic equilibrium is locally asymtotically stable if R0v > 1 and R0b > 1; pneumococcus endemic equilibrium is locally asymtotically stable if R0v < 1 and R0b > 1. Meanwhile, the co-infection endemic equilibrium is locally asymtotically stable if R0v > 1 and R0b > 1. From the numerical simulation result, it was shown that increasing the number of influenza A virus and pneumococcus made the number of population cell infected by influenza A virus and pneumococcus (co-infection) also increased.

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