To read this content please select one of the options below:

Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method

Ahmet Yıldırım (Department of Mathematics, Faculty of Science, Ege University, Bornova‐İzmir,Turkey)
Yves Cherruault (MEDIMAT, University PARIS 6, Paris, France)

Kybernetes

ISSN: 0368-492X

Article publication date: 16 October 2009

989

Abstract

Purpose

The purpose of this paper is to introduce an efficient method for solving susceptible‐infected‐removed (SIR) epidemic model. A SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine. The qualitative analysis reveals the vaccination reproductive number for disease control and eradication. It introduces homotopy perturbation method (HPM) to overcome these problems.

Design/methodology/approach

The paper considers HPM to solve differential system which describes SIR epidemic model. The essential idea of this method is to introduce a homotopy parameter, say p, which takes values from 0 to 1. When p=0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation. One of the most remarkable features of the HPM is that usually just few perturbation terms are sufficient for obtaining a reasonably accurate solution.

Findings

HPM is employed to compute an approximation to the solution of the non‐linear system of differential equations governing the problem.

Originality/value

The paper is of value in presenting, via some tables and figures, some numerical experiments which resulted from applying new methods on test problem.

Keywords

Citation

Yıldırım, A. and Cherruault, Y. (2009), "Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method", Kybernetes, Vol. 38 No. 9, pp. 1566-1575. https://doi.org/10.1108/03684920910991540

Publisher

:

Emerald Group Publishing Limited

Copyright © 2009, Emerald Group Publishing Limited

Related articles