Analysis of a tuberculosis model with undetected and lost-sight cases

• A tuberculosis model with undetected infectious and lost-sight cases is analyzed.
• The model exhibits the phenomenon of backward bifurcation.
• Backward bifurcation occurs only for high and unrealistic ranges of reinfection rates.
• For random values of the reinfection rates, the disease dies out.

A deterministic model of tuberculosis (TB) in sub-Saharan Africa including undetected and lost-sight cases is presented and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, when a stable disease-free equilibrium co-exists with one or more stable endemic equilibrium points when the associated basic reproduction number (R0R0) is less than unity. Analyzing the model obviously reveals that exogenous reinfection plays a key role on the existence of backward bifurcation. However, an analysis of the ranges of exogenous reinfection suggested that backward bifurcation occurs only for very high and unrealistic ranges of the exogenous reinfection rate. Random perturbation of reinfection rates was performed to gain insight into the role of this latter on the stability of the disease free equilibrium.