Epidemic Spreading and Control on Preferential Attachment Hypergraph with Community

The study of epidemic spreading in complex networks is fundamental to understanding diffusion processes across natural and social systems. While traditional graphs capture only pairwise interactions, many real-world processes involve higher-order group interactions that can be naturally represented by hypergraphs. In this work, we propose a community-based preferential attachment hypergraph model with tunable modularity and a heavy-tailed degree distribution, reproducing key structural properties in real systems. Based on this model, we develop a hypergraph-based SAIR framework to describe epidemic dynamics with asymptomatic transmission. A mean-field approximation is derived and compared with classical mean-field, heterogeneous mean-field, and Monte Carlo simulations, demonstrating improved predictive accuracy for community hypergraphs. The results show that epidemic spreading is regulated by community structure, transmission probability, and initial conditions, giving rise to localized, heterogeneous, and global diffusion regimes. By introducing a cross-community hyperedge index, we reveal that community structure suppresses spreading primarily through the reduction in inter-community transmission pathways. These factors collectively determine the spreading radius, propagation speed, and epidemic peak. We further evaluate behavioral, hyperedge-based, and node-based intervention strategies. Overall, this study provides a quantitative framework for analyzing epidemic spreading and control on community-structured hypergraphs, with potential relevance to studies of information diffusion and risk propagation.