Coupled Dynamics of Vaccination Behavior and Epidemic Spreading on Multilayer Higher-Order Networks.

Vaccination behavior and epidemic spreading are strongly intertwined processes, and their coevolution is often shaped by both individual decision-making and social interactions. However, most existing studies model such interactions at the pairwise level, overlooking the potential impact of higher-order social influence arising from group interactions. In this work, we develop a coupled vaccination-epidemic spreading model on multilayer higher-order networks, where vaccination behavior evolves on a simplicial complex and epidemic propagation occurs on a physical contact network. The model incorporates imperfect vaccine efficacy, allowing vaccinated individuals to become infected, and introduces a hybrid vaccination strategy that combines rational cost-benefit evaluation with social influence from both pairwise and higher-order interactions, as well as negative effects induced by vaccine failure. By constructing the coupled dynamical equations, we analytically derive the epidemic outbreak threshold and elucidate how higher-order interactions, behavioral responses, and vaccine-related parameters jointly affect epidemic dynamics. Numerical simulations on networks with different structural properties validate the theoretical results and reveal pronounced structure-dependent effects. The results show that higher-order social interactions can significantly reshape vaccination behavior and epidemic prevalence, while network heterogeneity and vaccine imperfection play crucial roles in determining the outbreak threshold and steady-state infection level. These results emphasize the necessity of incorporating higher-order interactions together with realistic vaccination behavior into epidemic modeling and offer new insights for the design of effective vaccination strategies.