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

Yulita Molliq Rangkuti¹, Syafruddin Side² & Mohd Salmi Md Noorani^3
 1Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Universitas Negeri Medan, Jalan Willem Iskandar,
Pasar V Medan Estate, Medan 20221, Indonesia
²Department of Mathematics, Faculty of Mathematics and Natural Sciences,
Universitas Negeri Makasar, Jalan A.P. Pettarani, Makasar90245, Indonesia
³School of Mathematical Sciences, Faculty of Science and Technology,
Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
Email: yulitamolliq@yahoo.com

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: Variational iteration method; homotopy perturbation method; SIR model; Lagrange multiplier; He’s polynomial