Higher-order interactions drive Turing–Hopf transitions and spatiotemporal patterns in epidemic networks

Understanding how infectious diseases spread across increasingly interconnected social and transportation systems remains a central challenge in contemporary epidemiology. Real-world epidemic outbreaks exhibit pronounced spatial heterogeneity and complex temporal dynamics, arising from the interplay among nonlinear population processes, diffusion mechanisms, and network structure. In this study, we examine how higher-order interactions, represented by simplicial complexes and hypergraphs, govern spatiotemporal pattern formation in a reaction–diffusion susceptible–infected (SI) epidemic model incorporating the Allee effect. By combining linear stability analysis with Turing bifurcation theory and codimension-two Turing–Hopf bifurcation analysis, we derive the critical conditions under which the system transitions from spatially homogeneous steady states to heterogeneous spatial patterns, synchronized oscillatory dynamics, and mixed spatiotemporal regimes. Our theoretical framework reveals that sparse higher-order structures amplify spatial heterogeneity by inducing diffusion-driven instabilities, whereas dense higher-order couplings suppress pattern formation and promote global synchronization. Moreover, hypergraphs exhibit broader instability regimes than simplicial complexes, because simplicial complexes enforce nested (downward-closure) topological constraints, whereas hypergraphs do not. Numerical simulations on random networks further demonstrate that connection probability regulates both the onset and saturation of spatial heterogeneity. These theoretical predictions are corroborated by real-world evidence derived from Chinese influenza surveillance data from 2023 to 2025 in conjunction with transportation network analysis. The results indicate that sparsely connected northern regions sustain localized heterogeneous outbreaks, whereas densely connected southern regions display synchronized epidemic waves. Taken together, these findings provide mechanistic insights into how higher-order network topology governs epidemic spreading patterns and highlight the potential of topology-informed public health strategies, including targeted interventions in sparsely connected regions and coordinated surveillance in highly coupled networks.