# Numerical analytic solution of SIR model of dengue fever diseasein South Sulawesi using homotopy perturbation method and variational iteration method

Yulita Molliq Rangkuti, Syafruddin Side, Mohd. Salmi Md. Noorani

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8 Citations (Scopus)

### 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.

Original language English 91-105 15 Journal of Mathematical and Fundamental Sciences 46 1 https://doi.org/10.5614/j.math.fund.sci.2014.46.1.8 Published - 2014

### Fingerprint

fever
dengue fever
Variational Iteration Method
Indonesia
dengue
Homotopy Perturbation Method
Dengue
Analytic Solution
iteration
perturbation
Lagrange multipliers
He's Polynomials
methodology
Polynomials
Model
polynomials
method
intervals
multipliers
Interval

### Keywords

• He's polynomial
• Homotopy perturbation method
• Lagrange multiplier
• SIR model
• Variational iteration method

• General

### Cite this

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title = "Numerical analytic solution of SIR model of dengue fever diseasein South Sulawesi using homotopy perturbation method and variational iteration method",
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.",
keywords = "He's polynomial, Homotopy perturbation method, Lagrange multiplier, SIR model, Variational iteration method",
author = "Rangkuti, {Yulita Molliq} and Syafruddin Side and {Md. Noorani}, {Mohd. Salmi}",
year = "2014",
doi = "10.5614/j.math.fund.sci.2014.46.1.8",
language = "English",
volume = "46",
pages = "91--105",
journal = "Journal of Mathematical and Fundamental Sciences",
issn = "2337-5760",
publisher = "Institute for Research and Community Services, Institut Teknologi Bandung",
number = "1",

}

TY - JOUR

T1 - Numerical analytic solution of SIR model of dengue fever diseasein South Sulawesi using homotopy perturbation method and variational iteration method

AU - Rangkuti, Yulita Molliq

AU - Side, Syafruddin

AU - Md. Noorani, Mohd. Salmi

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - He's polynomial

KW - Homotopy perturbation method

KW - Lagrange multiplier

KW - SIR model

KW - Variational iteration method

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