Numerical Analytic Solution of SIR Model of Dengue Fever Disease in South Sulawesi using Homotopy Perturbation Method and Variational Iteration Method

Yulita Molliq Rangkuti; Syafruddin Side; Mohd Salmi Md Noorani

doi:10.5614/j.math.fund.sci.2014.46.1.8

Authors

Yulita Molliq Rangkuti Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Medan
Syafruddin Side Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Makassar
Mohd Salmi Md Noorani School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia

DOI:

https://doi.org/10.5614/j.math.fund.sci.2014.46.1.8

Keywords:

Variational iteration method, homotopy perturbation method, SIR model, Lagrange multiplier, He�??s polynomial

Abstract

In this research, the susceptible"?infected"?recovered (SIR) model of dengue fever is considered. We have implemented two analytical techniques, namely the variational iteration method (VIM) and the homotopy perturbation method (HPM) for solving the SIR model. The Lagrange multiplier was investigated for the VIM and He's polynomial approach for the HPM was used. In these schemes, the solution takes the form of a convergent series with easily computable components. The resultsshow thatthe VIM solution is more accurate than the HPM solution for short time intervals, whereasthe HPM is more accurate than the VIM for long time intervalswhencompared with the fourth-orderRunge-Kutta method (RK4).We found that the HPM and the RK4 were in excellent conformance.

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