Fractional Age‐Structured Modeling of Measles: Application of Inverse Methods

This study introduces a novel fractional age‐structured Susceptibles‐Exposed‐Infective‐Hospitalized‐Recovered‐Adults (SEIHRA) model, designed to analyze measles transmission dynamics, particularly in younger populations. By incorporating age structure and an innovative inverse method, the model bridges mathematical rigor with empirical data. We examine equilibrium points, stability, and the basic reproduction number ( R 0 ), while using the inverse method to estimate the time‐dependent transmission rate β ( t ) from real‐world outbreak data. Validated with Chinese measles data (1974–2022), the model captures temporal and age‐specific trends, achieving an optimal fractional order of 0.94. Sensitivity analysis via the partial rank correlation coefficient (PRCC) technique highlights key parameters influencing R 0 . Combining age structure and inverse methods, this work reveals age‐specific transmission patterns and evaluates targeted vaccination strategies, offering critical insights for public health policies and global measles eradication efforts.