Analysis of the Stability of the Tuberculosis Disease Spread Model

This paper discusses the stability analysis of the model for the spread of tuberculosis and the effects of treatment. The authors analyze the dynamic behavior of the model to investigate the local stability properties of the model equilibrium point. The Routh-Hurwitz criterion is used to analyze local stability at the disease-free equilibrium point, while the Transcritical Bifurcation theorem is used to investigate the local stability properties of the endemic equilibrium point. The results of the discussion show that the stability properties of the equilibrium point depend on the value of the basic reproduction number which is calculated based on the Next Generation Matrix (NGM). When the basic reproduction number value is less than one, then the disease-free equilibrium point is locally asymptotically stable, whereas if it is more than one, then the endemic equilibrium point is locally asymptotically stable. Numerical simulations are included to explain the dynamic behavior of disease spread and to understand the effectiveness of tuberculosis treatment in a given population. The simulation results show that treatment in the infected individual phase is known to be more effective than treatment in latent individuals.