Identifying which age groups contribute most to uncertainty in disease transmission models is essential for improving model accuracy and guiding effective interventions. This study introduces an eigenvector-based sensitivity analysis framework that quantifies the influence of age-specific contact patterns on epidemic outcomes. By applying perturbation analysis to the Next Generation Matrix, we reformulate the basic reproduction number, R0, as a generalized eigenvalue problem, allowing us to pinpoint the age group interactions most critical to transmission dynamics. While the framework is broadly applicable to clinical outcomes such as hospitalizations, ICU admissions, and mortality, we focus here exclusively on the mortality outcome. We demonstrate the approach using two age-structured COVID-19 models with contact matrices from the UK and Hungary. Our results illustrate how differences in demographics, contact structures, and age group aggregations shape model sensitivity.