Abstract
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.
Highlights
In modern society, means of communication have developed very rapidly, and the spread of rumors basically relies on the new media of social networks. e flexibility of social media has greatly accelerated the speed of rumor propagating, which has exerted a great influence on People’s Daily life [1]
Adding true information spreader to the model, we have established ISTR model, and we have studied the dynamics of rumor propagation under the effect of social reinforcement
We have taken advantage of the characteristics of heterogeneous networks and have adopted a mean field method to solve the transformation probability of an ignorant person turning into a rumor spreader or a true information spreader and have calculated the mean field equation of the model
Summary
Means of communication have developed very rapidly, and the spread of rumors basically relies on the new media of social networks. e flexibility of social media has greatly accelerated the speed of rumor propagating, which has exerted a great influence on People’s Daily life [1]. In order to explore the law of rumor propagation on online social networks and formulate corresponding control strategies, Yu proposed 2I2SR rumor propagation model with and without delay based on multilingual environment [14]. Rough the calculation and analysis of the equilibrium point and basic reproduction number of the rumor model, Zhao et al proposed that the information released by the government and network monitoring can better prevent the propagating of rumors [32]. We consider the impact of social reinforcement and true information on rumor propagation dynamics and establish a rumor propagation ISTR model. E second part describes that, under the influence of social reinforcement, true information spreaders are added to the ISR model of rumor propagation and an ISTR model describing the rumor propagation dynamics. The simulation is used to verify the model and compare the changes of the model with or without control. e sixth part is conclusion
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