# Efficient Iterative Methods for Solving the SIR Epidemic Model

• Sawsan Mohsin Abed Department of Mathematics, College of Education for Pure Science (Ibn AL-Haytham), University of Baghdad, Baghdad, Iraq
• Majeed Ahmed AL-Jawary Department of Mathematics, College of Education for Pure Science (Ibn AL-Haytham), University of Baghdad, Baghdad, Iraq
Keywords: SIR epidemic model, Semi-analytical method, Daftardar-Jafari method, Temimi-Ansari method, Banach contraction method, Maximum error remainder

### Abstract

In this article, the numerical and approximate solutions for the nonlinear differential equation systems, represented by the epidemic SIR model, are determined. The effective iterative methods, namely the Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM), and the Banach contraction method (BCM), are used to obtain the approximate solutions. The results showed many advantages over other iterative methods, such as Adomian decomposition method (ADM) and the variation iteration method (VIM) which were applied to the non-linear terms of the Adomian polynomial and the Lagrange multiplier, respectively. Furthermore, numerical solutions were obtained by using the fourth-orde Runge-Kutta (RK4), where the maximum remaining errors showed that the methods are reliable. In addition, the fixed point theorem was used to show the convergence of the proposed methods. Our calculation was carried out with MATHEMATICAÂ®10 to evaluate the terms of the approximate solutions.

Published
2021-02-27
How to Cite
Abed, S. M., & AL-Jawary, M. A. (2021). Efficient Iterative Methods for Solving the SIR Epidemic Model. Iraqi Journal of Science, 62(2), 613-622. https://doi.org/10.24996/ijs.2021.62.2.27
Issue
Section
Mathematics  