Dynamics of Tuberculosis Transmission Model with Reinfection Issues

Abstract

Tuberculosis (TB) is a global epidemic caused by Mycobacterium tuberculosis. In this article, we study the dynamics of the TB transmission model with reinfection issues. It is demonstrated that the basic reproduction number R_0 defines the TB transmission dynamics. If R_0 < 1, only TB free equilibrium exists which is globally asymptotically stable, and when R_0 > 1, thus, there occurs endemic equilibrium, and the TB takes over. A bifurcation analysis was conducted by employing the bifurcation techniques of center manifold theory, both analytical and numerical solutions guarantee the occurrence of transcritical bifurcation at R_0 = 1. We also discussed the global stability of endemic equilibrium employing the approach of Lyapunov function. Numerical investigations illustrated that increase in reinfection value results in a huge force of infection. However, reinfection among treated individuals play an important role in the control of TB infection.