Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function

In daily lives, when emergencies occur, rumors will spread widely on the Internet. However, it is quite difficult for the netizens to distinguish the truth of the information. The main reasons are the uncertainty of netizens' behavior and attitude, which make the transmission rates of these information among social network groups being not fixed. In this paper, we propose a stochastic rumor propagation model with general incidence function. The model can be described by a stochastic differential equation. Applying the Khasminskii method via a suitable construction of Lyapunov function, we first prove the existence of a unique solution for the stochastic model with probability one. Then we show the existence of a unique ergodic stationary distribution of the rumor model, which exhibits the ergodicity. We also provide some numerical simulations to support our theoretical results. The numerical results give us some possible methods to control rumor propagation that (1)increasing noise intensity can effectively reduce rumor propagation when $\widehat{\mathcal{R}}_{0}>1$. That is, after rumors spread widely on social network platforms, government intervention and authoritative media coverage will interfere with netizens' opinions, thus reducing the degree of rumor propagation; (2) Speed up the rumor refutation, intensify efforts to refute rumors, and improve the scientific quality of netizen(i.e. increase the value of $\beta$ and decrease the value of $\alpha$ and $\gamma$ ) can effectively curb rumor propagation.

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

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.

Dynamic Analysis of a Stochastic Rumor Propagation Model with Regime Switching

We study the rumor propagation model with regime switching considering both colored and white noises. Firstly, by constructing suitable Lyapunov functions, the sufficient conditions for ergodic stationary distribution and extinction are obtained. Then we obtain the threshold Rs which guarantees the extinction and the existence of the stationary distribution of the rumor. Finally, numerical simulations are performed to verify our model. The results indicated that there is a unique ergodic stationary distribution when Rs>1. The rumor becomes extinct exponentially with probability one when Rs<1.

Dynamics of a Rumor Propagation Model with Stochastic Perturbation On Homogeneous Social Networks

The rapid development of information society highlights the important role of rumors in social communication, and its propagation has a significant impact on human production and life. The investigation of the influence of uncertainty on rumor propagation is an important issue in the current communication study. Due to incomprehension about others and the stochastic properties of the users' behavior, the transmission rate between individuals on social network platforms is usually not a constant value. In this paper, we propose a new rumor propagation model on homogeneous social networks from the deterministic structure to the stochastic structure. Firstly, a unique global positive solution of rumor propagation model is obtained. Then, we verify that the extinction and persistence of stochastic rumor propagation model are restricted by some conditions. IfR *0&lt; 1 and the noise intensity s i (i = 1,2,3) satisfies some certain conditions, rumors will extinct with a probability one. If R *0 &gt; 1, rumor-spreading individuals will continue to exist in the system, which means the rumor will prevail for a long time. Finally, through some numerical simulations, the validity and rationality of the theoretical analysis are effectively verified.

Correlation and trust mechanisms-based rumor propagation model in complex social networks

In real life, the process of rumor propagation is influenced by many factors. The complexity and uncertainty of human psychology make the diffusion model more challenging to depict. In order to establish a comprehensive propagation model, in this paper, we take some psychological factors into consideration to mirror rumor propagation. Firstly, we use the Ridenour model to combine the trust mechanism with the correlation mechanism and propose a modified rumor propagation model. Secondly, mean-field equations which describe the dynamics of the modified SIR model on homogenous and heterogeneous networks are derived. Thirdly, a steady-state analysis is conducted for the spreading threshold and the final rumor size. Fourthly, we investigate rumor immunization strategies and obtain immunization thresholds. Next, simulations on different networks are carried out to verify the theoretical results and the effectiveness of the immunization strategies. The results indicate that the utilization of trust and correlation mechanisms leads to a larger final rumor size and a smaller terminal time. Moreover, different immunization strategies have disparate effectiveness in rumor propagation.