Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method
Makaleler > Tam Makale · 2009
Yazarlar: Ahmet YILDIRIM, Yves CHERRUAULT
Kybernetes, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2009, cilt 38, ss 1566-1575
DOI: 10.1108/03684920910991540
Özet
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.