The accuracy comparison of the RK-4 and RK-5 method of SEIR model for tuberculosis cases in South Sulawesi

Abstract

This research discusses about the accuracy of the 4th and 5th order Runge-Kutta methods (RK-4 and RK-5) as a numerical solution in the Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model of Tuberculosis (TB) transmission in South Sulawesi. The data used are secondary data on the number of TB patients in South Sulawesi sourced from the South Sulawesi Health Office. The research begins by further examining the SEIR model on TB transmission, then looking for general solutions of the SEIR model with the 4th-order and 5th-order Runge-Kutta methods, parameter determination, simulation and results analysis. In this research, the movement graph is obtained from the SEIR model with real data. After analysing the numerical simulation, the accuracy of the 4th-order and 5th-order Runge-Kutta methods is compared, then the two methods are compared to observe a more accurate method. The result of this research shown that the simulation of SEIR model is accurate to predict TB cases in South Sulawesi. The Runge-Kutta method can used to observe trends in the spread of TB in South Sulawesi. The numerical simulation shown that the 5th-order more accurate than the 4th-order Runge-Kutta methods. The results of the modelling are simulated using Maple can predict the number of TB cases which can be used by the government as a consideration to prevent the spread of TB in South Sulawesi.