Backward bifurcation in a mathematical model for tuberculosis with loss of immunity

A mathematical model is developed to study the impact of loss of immunity on the transmission dynamics of tuberculosis (TB). Center manifold theory is applied to show that a backward bifurcation may occur under certain conditions, that is, a stable endemic steady-state may exist for R0 \u3c 1. For a simplified model, it is shown that the unique endemic equilibrium is locally asymptotically stable if R 0 \u3e 1. Sensitivity and uncertainty analysis using Latin Hypercube Sampling (LHS) method are presented to evaluate the variability of the model outcomes as a result of alternating parameter values, and to determine which parameters play key roles in producing the observed variability. Stochastic simulations are also performed