A Rumor Dissemination Control Model Based on Evolutionary Game and Multiple User States

Rumor spreading in social networks involves complex dynamic causes. This paper constructs a new rumor spreading dynamics model based on evolutionary game theory to account for the possible skepticism of users during the dissemination of rumors, and introduces control theory for the directional management of public opinion in social networks. Firstly, based on the infectious disease dynamics model, we introduce users who exhibit skepticism when exposed to rumor information and continue to pay attention to it, classifying them as in a rumor-suspecting state during the rumor propagation process. Taking into account the impact of rumor information on users, as well as their intrinsic tendency to seek profit in the face of rumors, we quantify the influence of rumor news. This paper innovatively introduces the “rumor-suspecting state” into the traditional rumor propagation model, enabling a more comprehensive representation of skeptical user behaviors during rumor dissemination. By combining this with evolutionary game theory, we construct the driving force mechanism for users' rumor propagation, providing a foundation for understanding the transformation of users' states within the rumor-suspecting context. Secondly, to reduce the impact of rumor information and limit its spread, we develop a hybrid control strategy that combines two approaches: prevention and isolation. After implementing these hybrid control measures, we address the imbalance between control costs and effectiveness by establishing an optimal control problem with constraints. This aims to achieve optimal control with time-varying properties, and we theoretically derive the optimal solution to minimize costs. Finally, considering the complexity of rumor information and the need for effective rumor control, we propose an improved model of rumor propagation dynamics that combines the infectious disease model with optimal control theory. This model defines state transfer equations based on multiple user states and optimal control.The effectiveness of the control strategy is validated through theoretical proofs and experiments, and the impact of various factors on information diffusion is analyzed. On a real dataset we show that the model can effectively explain the diffusion process of complex rumor information in the network and manage it.