The Role of Re-Infection in Modeling the Dynamics of One-Strain Tuberculosis Involving Vaccination and Treatment

In this article a continuous time deterministic model with vaccination and treatment strategies is formulated to assess the effect of reinfection on the transmission dynamics of Tuberculosis (TB). The involvement of reinfection in our model causes relapse and leads to the possibility of backward bifurcation at critical value of effective reproduction number R e =1 and hence the existence of multiple equilibria when effective reproduction number R e <1. This indicates that even by reducing effective reproduction number R e  below one is no longer a sufficient condition to eradicate the disease from community. An additional reduction of effective reproduction number R e  below the saddle-node bifurcation value is required to eradicate disease from community provided that the disease free equilibrium is globally asymptotically stable. Numerical simulation results are presented to validate analytical results. We suggest that reinfection is an important feature of TB and has to be considered when modeling the complex dynamics of TB.