Information dissemination refers to how information spreads among users on social networks. With the widespread application of mobile communication and internet technologies, people increasingly rely on information on the internet, and the mode of information dissemination is constantly changing. Researchers have performed various studies from mathematical modeling and cascade prediction perspectives to explore the previous problem. However, lacking a comprehensive review of the latest information dissemination models hinders scientific development. As a result, it is essential to review the latest models or methods. In this paper, we review information dissemination models from the past three years and conduct a detailed analysis, such as explanatory and predictive models. Moreover, we provide public datasets, evaluation metrics, and interface tools for researchers focusing more on algorithm design and modeling. Finally, we discuss the model application and future research directions. This paper aims to understand better the research progress and development trends for beginners and guide future research endeavors. We believe this article will attract more researchers’ interest and attention to the information dissemination field on social networks.

Information diffusion prediction aims to predict the next infected user in the information diffusion, which is a critical task to understand how information spreads on social platforms. Existing methods mainly focus on the sequences or topology structure in euclidean space. However, they fail to sufficiently consider the hierarchical structure or power-law structure of the underlying topology of information cascade graphs and social networks, resulting in distortion of user features. To tackle above issue, we propose an innovative Constrained Temporal Hypergraphs and Graph Neural Networks (THGNets) framework that is tailored for information diffusion prediction. Specifically, we introduce hyperbolic temporal hypergraphs neural network to alleviate the distortion of user features by hyperbolic hierarchical learning in information cascades. Additionally, it also captures high-order dynamic interaction patterns between users and further integrates the time-consistency constraint mechanism to mitigate the instability and non-smoothness of user features in latent space. In parallel, we apply the hyperbolic graph neural network to investigate the hierarchical structure and user homogeneity on social networks, enhancing our understanding of social relationships. Moreover, hyperbolic gated recurrent units are employed to capture the potential dependency relationships between contextual users. Experiments conducted on four public datasets demonstrate that the proposed THGNets significantly outperform the existing methods, thereby validating the superiority and rationality of our approach.

Rumor spreading on social media platforms can significantly impact public opinion and decision-making. In this paper, we proposed an innovative ignorant-spreader-expositor-hibernator-remover (ISEHR) rumor-spreading model with multivariate gatekeepers. Specifically, by analyzing the model's dynamics, we identified the critical threshold that determined the persistence or extinction of rumor spreading. Moreover, we applied the Routh-Hurwitz judgment, Lyapunov theory, and LaSalle's invariance principle to investigate the existence and stability of the rumor-free/rumor equilibrium points. Furthermore, we introduced the optimal control to alleviate rumor spreading with the multivariate gatekeeper mechanism. Finally, extensive numerical simulations validated our theoretical findings, providing insights into the complex dynamics of rumor spreading and the effectiveness of the proposed control measures. Our research contributes to a deeper understanding of rumor spreading on social networks, offering valuable implications for the development of effective strategies to combat rumor.