Prediction of Tuberculosis Disease Using SIR Model with Implementation of Runge-Kutta Method in Malaysia

Abstract

 The purpose of this paper is to anticipate the rate of tuberculosis disease transmission by contrasting two scenarios: one with and one without demography. This paper involved the application of Susceptible-Infected-Recovered (SIR) mathematical model, SIR model with implementation of Fourth Order Runge-Kutta method in order to analyse the number of individuals in three compartments: susceptible, infected and recovered. Furthermore, this paper examined tuberculosis disease prediction by comparing two SIR models and percentage of error by comparing to actual data. The least percentage error model will be chosen to proceed with the prediction of tuberculosis incidence rate for each 100,000 people in Malaysia for 2022. Next, the value of parameters for transmission rate, β and recovery rate, γ, are varied in order to see the effect on incidence rate value. As a result, it was found that SIR model with demography was more accurate and applicable to use as a prediction model for tuberculosis disease. It was also shown that the number of people reported at the peak of the graph decreases with the decrease in transmission rate. Meanwhile, at the end of the year, the incidence rate per 100,000 individuals increased with a reduced transmission rate and a higher incidence rate per 100,000 individuals regardless of recovery rate. Thus, it can be concluded that these variables give significant impact in determining the incidence rate of tuberculosis.