Coevolution of multipathogens on higher-order networks

The spreading dynamics of multipathogens are not independent in higher-order complex systems, but often involve synergistic, competitive, and asymmetric interactions among pathogens. As such interactions emerge, a high-dimensional nonlinear dynamical system arises, requiring a coevolutionary framework to describe its patterns. To explain the coevolution of pathogens A and B on higher-order networks, we propose a mathematical model and develop a degree-weighted dimension-reduction approach that compresses the original 2N-dimensional system into a two-dimensional effective one. Through theoretical analysis and numerical simulations, we verify the consistency of steady states before and after dimension reduction, obtaining an analytically tractable phase diagram. The results show that higher-order interactions and synergistic effects substantially shape multipathogen dynamics. Specifically, stronger higher-order interactions reduce presence thresholds, promote competitive exclusion, and suppress synergy, whereas stronger synergistic strength lowers absolute thresholds and facilitates coexistence by enhancing mutual reinforcement. Phase diagram analysis further identifies multiple dynamical regions, including bistability, hysteresis, coexistence, and alternating dominance. Moreover, the asymmetric case reveals that the interplay between higher-order infection intensity and synergistic strength fundamentally determines whether competition or synergy dominates the system. Overall, this work establishes a systematic theoretical framework for analyzing how multipathogen interactions shape dynamical processes on higher-order networks.