Global stability of SIR and SEIR model for tuberculosis disease transmission with lyapunov function method

Abstract

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 R0 also be obtained from the two models, namely, if R0>1 then obtained asymptotically stable equilibrium endemic globally and if the basic reproduction number R0≤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.