Effect of the Vaccine on the Dynamics of Speread of Tuberculosis SIR Models

Abstract

Tuberculosis (TB) is an infectious disease that is very dangerous and can cause death and Tuberculosis (TB) is an infectious disease that causes the most deaths or is called the world's biggest killer among infectious diseases, claiming more than 4000 lives every day. The unprecedented Corona Virus pandemic has a serious impact on people with pre-existing health conditions such as Tuberculosis. Tuberculosis is not caused by heredity and Tuberculosis is curable. Treatment of TB disease is time-consuming and costly. Therefore the term prevention is better than cure very precisely for Tuberculosis. One of the efforts made by the government is to provide vaccines. This study uses the SIR (susceptible, infected, and recovered) model by considering the effect of vaccines. Also, this study adopts the application of the Optimum Control theory which aims to provide control over the parameters that affect the spread of Tuberculosis. The purpose of this study is not only to show the dynamics of the spread of tuberculosis but also to see to what extent the effect of vaccines reduces the spread of tuberculosis. And how does the optimal control theory influence the spread of tuberculosis?This research is proposed to estimate the basic reproduction number (R0) from the dynamics of the Tuberculosis epidemic. The basic reproductive number ((R0) is often used as a threshold parameter to determine the boundary betweenextinction and endemic. If R0<1 indicates the dengue virus will become extinct and if R0> 1 shows the Tuberculosis is endemic. By considering vaccines identified a slowing of the spread of tuberculosis.