One tuberculosis transmission model is formulated by incorporating exogenous reinfection, relapse, and two treatment stages of infectious TB cases. The global stability of the unique disease-free equilibrium is obtained by applying the comparison principle if the effective reproduction number for the full model is less than unity. The existence and stability of the boundary equilibria are given by introducing the invasion reproduction numbers. Furthermore, the existence and local stability of the endemic equilibrium are addressed under some conditions. Keywords: Exogenous reinfection; relapse; the effective reproduction number; the invasion reproduction number; center manifold theory; stability. 1250031-1 Int. J. Biomath. 2012.05. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/25/15. For personal use only. L. Liu & X. Gaoamong patients in the 2007 cohort, 87% were successfully treated, which is the first time the target of 85% has been exceeded at the global level [36]. But, almost 30,000 cases of multidrug-resistant TB (MDR-TB) were notified in 2008, which is equivalent to 11% of the total number of cases of MDR-TB estimated to exist among cases notified in 2008 [36], which is currently a main threat to tuberculosis control programs and community health [31].MDR-TB is thought to be a formidable challenge to global TB control in several settings, but until now, the global burden is largely unknown [38]. It was roughly estimated that the number of the MDR-TB cases in India, China and Russia accounted for more than 62% of the global MDR-TB burden [6,38]. It was reported in China that the prevalence of MDR-TB among TB patients with diagnosis ranged from 4.5% in Zhejiang Province to 10.8% in Henan Province [15]. The main cause of developing MDR-TB is thought of as due to the incomplete treatment of infectious TB cases by adopting the Directly Observed Treatment, Short-Course (DOTS) strategy recommended by WHO. Actually, the failure treatment of infectious TB cases maybe result in the emergence of drug-resistant strains in the body and the relapse of recovered individuals. Furthermore, drug-resistant strains can cause much higher mortality rates, treatment failure, and relapse, and treatment is more toxic, expensive, and lengthy [8,12,14].Active tuberculosis in TB patients with previous tuberculosis infection can be due to either the endogenous reactivation by the same strain or the exogenous reinfection by a new strain. The issue of the role of exogenous reinfection has been debated for decades [1,4,33]. It is commonly thought that incomplete treatment, either regimen or treatment duration, is the very important cause for relapse. However, a study in Shanghai, China, indicated that exogenous reinfection accounted for 61.5% of the recurrent TB cases, which also indicated that high levels of transmission of M. tuberculosis were an important cause of TB in Shanghai, China [24]. Furthermore, in a 2003 review [13], one study supported that the exogenous reinfection in HIV-infected patien...