Unraveling the role of higher-order interactions in vaccinated VIS epidemics via simplicial modeling

Abstract To more accurately capture the clustering dynamics in disease transmission, this paper introduces a novel vaccinated simplicial contagion model that incorporates higher-order interactions. By utilizing simplicial complexes, the model represents not only dyadic contacts but also group-level transmission pathways (e.g., gatherings), offering a more realistic representation of contagion in structured populations. Through a quenched mean-field framework, we derive dynamical equations governing the states of nodes (vaccinated, susceptible, infected) and establish analytical conditions for equilibrium stability and the epidemic threshold. Our results show that higher-order interactions markedly reduce the critical transmission threshold and can induce bistability—coexistence of persistent periodic outbreaks and a disease-free state—especially when vaccine-derived immunity wanes or vaccination coverage among susceptibles crosses critical thresholds. Sensitivity analyses reveal that pairwise transmission correlations significantly influence the epidemic threshold, whereas semi-sensitivity analysis identifies vaccination rate in the susceptible population as the most impactful parameter, emphasizing the coupling between higher-order social contagion and vaccination efforts. Numerical simulations validate that increased waning immunity, higher recovered-but-unvaccinated fractions, and decreased vaccination or recovery rates trigger a transition from forward to backward bifurcation, accompanied by bistable dynamics. These findings highlight the pivotal role of higher-order interactions in driving complex epidemic phenomena and offer theoretical guidance for designing multi-scale intervention strategies that target both group and individual-level spread.