Routh-hurwitz criterion and bifurcation method for stability analysis of tuberculosis transmission model

Abstract

Tuberculosis is an infectious disease; it caused by Mycobacterium tuberculosis. In this paper, we discuss how to use the Routh-Hurwitz stability criterion to analyze the stability of disease free of the tuberculosis transmission model. From this method, can be found the number of roots of the characteristic polynomial (eigenvalues) with positive real parts is equal to the number of changes in sign of the first column of the Routh array. If all of the eigenvalues are negative, then the model is stable. While the bifurcation method is used to analyze the stability of the endemic equilibrium point of the tuberculosis transmission, the endemic equilibrium point is locally asymptotically stable if reproduction number greater than one and additional parameters requirement that bifurcation met. Finally, numerical simulations are demonstrated to verify the used method.