Transmission of Tuberculosis and Reproduction Number Using Lyapunov Function of SIR Model

This paper studies the mechanism of transmission Tuberculosis (TB) caused by mycobacterium tuberculosis bacteria. TB is an airborne disease that endangering human population globally. Mathematical modelling was developed using Susceptible-Infected-Recovered (SIR) model in this analysis. The generated four-dimensional, nonlinear dynamic system reduced to three dimensions, with some assumptions. Then, will be analyzed creating a mathematical theorem prove existence event, disease-free equilibrium phase, and endemic stage. By Lyapunov function method, theorems can proved. basic reproduction number R0 also obtained from model. If ≤ 1, then global asymptotically stable if > Carrying out simulation data selected region, result successfully describes forecast cases it may used for assessing status.