Numerical Solution of SIR Model for Tuberculosis Transmission using Homotopy Perturbation Method in South Sulawesi
Syafruddin Side(a*), Muh. Isbar Pratama(b), Nur Rezky Ramadhan(c), and Wahidah Sanusi(a)

a)Department of Mathematics Universitas Negeri Makassar
*syafruddin[at]unm.ac.id
b)Department of Mathematics, Universitas Muhammadiyah Bulukumba
c)Department of Mathematics, Bosowa University

Abstract

The aims of this study are to analysis and find the numerical solution of the Susceptible-Exposed-Infected-Recovered (SIR) model of Tuberculosis (TB) transmission in South Sulawesi. The data used is secondary data on the number of TB patients in South Sulawesi. The discussion begins with a further study of the SIR model, then looks for a general solution to the SIR model using the Homotopy Perturbation Method. Parameter determination, simulation and analysis of results in this study obtained a graph of the movement of the SIR model with real data. After analyzing numerical simulations, it can be seen that the Homotopy Perturbation Method can be used to see the trend of the spread of TB in South Sulawesi. The results showed that the SIR model on TB transmission is a three-dimensional non-linear differential equation. The prediction results of the SIR model of TB transmission using the homotopy perturbation method show that the number of TB cases in South Sulawesi is increasing every year so that early prevention measures are the government^s attention to prevent the spread of TB in South Sulawesi.

Keywords: SIR model- tuberculosis- Analysis and simulation- Homotopy Perturbation Method

Topic: Mathematics