Imperfect vaccination and coupled epidemic dynamics in age-structured multiplex networks

Vaccination behavior is closely coupled with disease transmission through individual risk perception and age-dependent contact patterns. However, the combined effects of imperfect vaccine protection and age-specific mixing on behavior-epidemic dynamics remain insufficiently characterized. We develop a network-based dynamical model that couples susceptible-infected-recovered-vaccinated (SIRV) transmission with an evolutionary vaccination game. Empirical age-specific contact matrices are used to represent interactions among age groups and to examine how contact heterogeneity shapes vaccination behavior and disease transmission. Approximate theoretical analysis and stochastic simulations indicate that vaccination uptake depends on the balance between individual protection and population-level feedback. When vaccine efficacy is high, individual incentives are stronger and promote higher vaccination coverage. When efficacy is low, population-level feedback becomes more important for limiting free riding. Age-structured contacts further amplify inter-group differences, with highly connected age groups showing higher vaccination uptake and a stronger effect on epidemic outcomes. These results identify age-specific contact patterns as a key structural factor in behavior-transmission coupling. The proposed framework provides a basis for studying immunization strategies in structured populations.