Dynamical systems analysis of tuberculosis with the impact of transmission rate and vaccination.

This paper examine the impact of transmission rate and vaccination on the dynamics of tuberculosis infection. Model analysis is established, the existence of hopf-bifurcation is analytically shown which deduces the oscillatory persistence of the infection in the population. The stability properties of the steady states and its bifurcation structures are investigated. We illustrate that there exist threshold values for the transmission rate and vaccination which corresponds to saddle node, transcritical and subcritical hopf bifurcation.