Global Stability of SIR and SEIR Model for Tuberculosis Disease Transmission with Lyapunov Function Method

Background and Objective: Tuberculosis (TB) is an infectious disease that poses a threat to the human population in the world.The aimed of study discussed are to build a model SIR and SEIR tuberculosis disease transmission and analysis for both models.Methodology: The SIR model is a system of ordinary differential equations four dimension and SEIR model is a system of ordinary differential equations five dimension.Both models are then analyzed by building a mathematical theorem, which guarantees the existence of a case of TB, the disease-free equilibrium phase and stage of disease endemic TB.Results: Three theorems proving using the Lyapunov function method.Basic reproduction number R 0 also be obtained from the two models, namely, if R 0 >1 then obtained asymptotically stable equilibrium endemic globally and if the basic reproduction number R 0 #1, acquired the disease-free equilibrium global asymptotically stable.Conclusion: The results of both models can be used to determine the status of TB disease in a region by conducting a simulation using data in the region.