SEIR Epidemic Model of the Spread of Tuberculosis in Samarinda City with the Addition of Vaccination Parameters

Abstract

Tuberculosis (TB) is a contagious, dangerous disease that infects the human body through the respiratory tract. The city of Samarinda itself is the city with the second highest rate of tuberculosis transmission in East Kalimantan. The aim of this research is to build a SEIR mathematical model of the spread of tuberculosis, analyze the stability of the model, and simulate the model. This research uses the Runge-Kutta method, which has high accuracy in estimating solutions and is relatively stable. This data is secondary data obtained through BPS as well as articles from previous researchers. The results of the research showed that the percentage of increase in the spread of the virus in the susceptible population (S) during the first week was 2,048%, then the 4th week to the 100th day decreased by approximately 164,100%, then the percentage of the population that was exposed but did not spread it (E) decreased in the first week, namely 34,525%, then in the 4th week to the 100th day there was a very significant decrease, namely 7,600%, then the percentage of the population infected and infectious (I) in the first week rose to 19,138%, then in the 4th week to the 2nd week -100 experienced a decrease of approximately 716,900%, and finally, the percentage of the population who recovered in the first week began to increase due to the very influential vaccine, namely increasing by 26,860%, then the 4th week to the 100th week also experienced a significant increase, namely by 81.681%.