Hyperedge size-driven multiscale epidemic dynamics on hypergraphs

Infectious diseases pose a significant threat to global health security. Higher-order networks have recently emerged as a powerful framework to capture group-based transmission processes. Conventional studies often assume that transmission probabilities scale with group size; however, such probabilities may in fact remain constant due to intrinsic epidemiological properties. In other words, the apparent variation of transmission probabilities may instead arise from additive effects which may stem from time scale variations for various group sizes based on the existing studies. The group-size based multiscale influence on the dynamics is unclear. To elucidate this mechanism, we propose a multiscale epidemic model on hypergraphs incorporating two- and three-body interactions, where transmission intensities are used to unify heterogeneous temporal scales. Two extreme mechanisms are analyzed: individual and group transmission models. We derive the basic reproduction number R0 and perform bifurcation analysis. Our results reveal that R0 depends on both pairwise and triadic transmission intensities and yields only forward bifurcation in individual transmission, whereas in group transmission R0 depends solely on the latter but exhibits backward bifurcation. Subsequently, Monte Carlo simulations validate the models' rationality and further numerical simulations demonstrate that triadic transmission intensity markedly alters the basic reproduction number, steady states, and region distributions of the solutions. These findings highlight how additive effects of group interactions drive multiscale epidemic dynamics, offering new insights into higher-order mechanisms underlying infectious disease spread.