APPLICATION OF THE VARIATIONAL ITERATION METHOD TO A FRACTIONAL-ORDER SEIR MEASLES EPIDEMIC MODEL

Abstract

This paper presents a robust numerical approach for solving a sys- tem of nonlinear fractional differential equations representing an SEIR measles epidemic model. The model incorporates Caputo fractional derivatives to capture the memory effects and complex dynamics of disease transmission more accurately than classical integer-order models. We employ the Variational Iteration Method (VIM), a powerful analytical technique that does not require perturbation or linearization, to obtain approximate analytical solutions. The stability analysis of the disease-free equilibrium is conducted. The efficiency and accuracy of the proposed VIM scheme are demonstrated through detailed numerical simulations at different fractional orders. A comparative analysis with the Laplace Adomian Decomposition Method (LADM) and the classical Differential Transform Method (DTM) highlights the advantages of VIM in terms of convergence and reliability. The results, presented through extensive tables and graphs, show that VIM pro- vides a highly effective tool for analyzing the dynamics of fractional- order epidemiological systems.