Spatiotemporal heterogeneity of a network epidemic model with higher-order interactions and advection mechanisms

Abstract Reaction–diffusion infectious disease models are widely used to describe the spatial distribution of infected individuals. In this study, we construct network-based reaction–diffusion models that incorporate both higher-order interactions and advection mechanisms, formulated on a triangular lattice torus network. This idealized structure is adopted to facilitate explicit derivation and linear stability analysis of the theoretical conditions for Turing instability—analyses that would be considerably more challenging in complex heterogeneous geometries. To address the computational challenge of generating higher-order node Laplacian matrices in large-scale networks, we develop a dimensionality reduction strategy using graph-structured edge Laplacians. The theoretical analysis reveals how higher-order interactions and advection jointly influence the onset of Turing patterns. Furthermore, model fitting to real epidemic data—using a mobility network constructed from 2020 inter-prefectural commuting flows across Japan’s 47 prefectures—shows that incorporating higher-order interactions results in better fitting performance compared to conventional models.