HOMOTOPY PERTURBATION METHOD FOR SOLVING A NONLINEAR SYSTEM FOR AN EPIDEMIC

Nada  A. M. Alshomrani; Weam  G. Alharbi; Ibtisam  M. A. Alanazi; Lujain  S. M. Alyasi; Ghadi  N. M. Alrefaei; Seada  A. Al’amri; Asmaa  H. Q. Alanzi

Nada A. M. Alshomrani Department of Mathematics Faculty of Science University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
Weam G. Alharbi Department of Mathematics Faculty of Science University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
Ibtisam M. A. Alanazi Department of Mathematics Faculty of Science University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
Lujain S. M. Alyasi Department of Mathematics Faculty of Science University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
Ghadi N. M. Alrefaei Department of Mathematics Faculty of Science University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
Seada A. Al’amri Department of Mathematics Faculty of Science University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
Asmaa H. Q. Alanzi Department of Mathematics Faculty of Science University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia

Article ID: 2442

Keywords: ordinary differential equation, homotopy perturbation method, initial value problem, series solution

Abstract

This paper solves the SIR-epidemic model utilizing the homotopy perturbation method (HPM). The HPM is applied in a different way in contrast to the HPM in the literature. The current approach uses a new canonical form for the system of the SIR-epidemic. The analytic solution is obtained and compared with the published one, in addition, to the Runge-Kutta numerical method. The results show better accuracy than the corresponding ones.

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