A new model for MDR-TB infection with undetected TB cases

This paper describes a mathematical model for tuberculosis (TB) and discusses its dynamic behavior. The model is novel in that it combines multi-drug resistant TB (MDR-TB) with undetected TB cases. The basic reproduction number, R₀, is calculated. The result shows that the disease-free equilibrium is globally asymptotically stable if R₀ ≤ 1, and is unstable if R₀ > 1. When R₀ > 1, there also exists a locally asymptotically stable endemic equilibrium. Simulations confirm the analysis, and exhibit that undetected TB cases play an important role.