Backward bifurcation analysis on Tuberculosis disease transmission with saturated treatment

In this research article, the authors intend to introduced an SEI (Susceptible-Exposed-Infectious) Tuberculosis model to consider the limitation of medical resources using a saturated treatment function. This is important to analyze the effect of hospital capacity in the success of Tuberculosis prevention strategy. Mathematical analysis was conducted to determine and analyze the existence and local stability criteria for equilibrium points, and how they related to the basic reproduction number of the model. The stability criteria of the endemic equilibrium point were analyzed using the center manifold theory. Our analysis showed that the saturated treatment rate might lead our proposed model to exhibit backward bifurcation at a basic reproduction number equal to one, and this phenomena appears related to the size of the treatment saturated parameter. Local sensitivity analysis was given to give a suggestion about how to avoid the occurrence of backward bifurcation phenomena. To support our analytical results, some simulations were presented at the end of the work.