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The qualitative analysis reveals the vaccination reproductive number for disease control and eradication. It introduces homotopy perturbation method (HPM) to overcome these problems.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>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 <jats:italic>p<\/jats:italic>, which takes values from 0 to 1. When <jats:italic>p<\/jats:italic>=0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As <jats:italic>p<\/jats:italic> 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.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>HPM is employed to compute an approximation to the solution of the non\u2010linear system of differential equations governing the problem.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The paper is of value in presenting, via some tables and figures, some numerical experiments which resulted from applying new methods on test problem.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910991540","type":"journal-article","created":{"date-parts":[[2009,10,17]],"date-time":"2009-10-17T07:04:10Z","timestamp":1255763050000},"page":"1566-1575","source":"Crossref","is-referenced-by-count":40,"title":["Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method"],"prefix":"10.1108","volume":"38","author":[{"given":"Ahmet","family":"Y\u0131ld\u0131r\u0131m","sequence":"first","affiliation":[]},{"given":"Yves","family":"Cherruault","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022012820423732700_b20","unstructured":"Arrowsmith, D.K. and Place, C.M. 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