Improved Variational Iteration Solutions to the SIR Model of Dengue Fever Disease for the Case of South Sulawesi

Sudi Mungkasi (Department of Mathematics, Faculty of Science and Technology, Sanata Dharma University, Paingan, Maguwoharjo, Depok, Sleman, Yogyakarta 55282)

Journal of Mathematical and Fundamental Sciences
Vol. 52 No. 3 (2020)

The susceptible-infected-recovered (SIR) model of the spread of dengue fever for the case of South Sulawesi is considered. Rangkuti's variational iteration method (RVIM) is recalled. This paper makes four contributions. The first one is to provide a successive approximation method (SAM) for solving the considered model. The second one is to show that SAM and RVIM are identical. Thirdly, a modification of RVIM is proposed. Fourthly, it is shown that the modification leads to an improvement of the accuracy of the method. Both RVIM and the improved version are quite accurate for short time periods. However, the improved version is more accurate and is able to provide more realistic explicit solutions to the model.