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

## TL;DR

This paper studies how vaccination decisions and disease spread interact in complex social networks, showing that group influences and network structure strongly affect epidemic outcomes.

## Contribution

The novel contribution is a coupled model of vaccination behavior and epidemic dynamics on multilayer higher-order networks, incorporating imperfect vaccines and social influence from group interactions.

## Key findings

- Higher-order social interactions significantly reshape vaccination behavior and epidemic prevalence.
- Network heterogeneity and vaccine imperfection strongly influence the outbreak threshold and steady-state infection levels.
- The model reveals structure-dependent effects validated through numerical simulations.

## Abstract

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.