Understanding Measles Contagion: A Fractional‐Order Model With Stability and Sensitivity Insights

In this paper, we propose an epidemiological mathematical model described by a system of nonlinear differential equations of fractional order (FODEs). Specifically, we employ the Caputo fractional derivative (CFD). Our analysis verifies the existence of a solution. Furthermore, we investigate the model’s global stability by analyzing the stability of the equilibrium points. Additionally, we calculate the basic reproduction number ( R 0 ) to assess the potential for measles transmission. In the numerical section, we perform a sensitivity analysis of the reproduction number, examining how changes in model parameters impact disease dynamics. Moreover, we employ a decision tree approach to investigate the impact of variations in ( ε ) and ( R 0 ) on disease outcomes.