Sensitivity stability and feasibility analysis of epidemic measles using mathematical SEIR model

The present study investigates the measles pandemic using a time-varying SEIR model. The study identifies endemic equilibrium points, disease-free equilibrium points, and basic reproduction numbers for both time-varying and time-invariant SEIR models, comparing their impacts on partition transitions. The study confirms the measles model’s asymptotic stability at the disease-free equilibrium point, both locally and globally. Sensitivity analysis of parameters is conducted to propose strategies for disease control and validate the model’s applicability. Additionally, an analytical solution employing the Homotopy perturbation method is derived, complemented by numerical solutions using the Euler method, with comparative analysis of results between the methods. Finally, sensitivity indices for both time-varying and time-invariant reproduction numbers are determined and compared.