Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation

We propose and analyze a mathematical model for tuberculosis (TB) transmission to study the role of exogenous reinfection and endogenous reactivation. The model exhibits two equilibria: a disease free and an endemic equilibria. We observe that the TB model exhibits transcritical bifurcation when basic reproduction number R-0 = 1. Our results demonstrate that the disease transmission rate beta and exogenous reinfection rate a plays an important role to change the qualitative dynamics of TB. The disease transmission rate beta give rises to the possibility of backward bifurcation for R-0 < 1, and hence the existence of multiple endemic equilibria one of which is stable and another one is unstable. Our analysis suggests that R-0 < 1 may not be sufficient to completely eliminate the disease. We also investigate that our TB transmission model undergoes Hopf-bifurcation with respect to the contact rate beta and the exogenous reinfection rate alpha. We conducted some numerical simulations to support our analytical findings. (C) 2018 Published by Elsevier B.V.