The Asymptotical Behaviors Of Models For Tuberculosis With Vaccination And Drug-Resistance

Tuberculosis (TB) is an ancient disease harmful to human life and health. China is a high TB-burden country of which the infectious tuberculosis epidemic is very serious. In recent years, the TB prevalence status become serious because of the numerous immigration, environmental changes and the spread of drug-resistant TB, the incidence is trending to rapidly ascend. In1995, the World Health Organization (WHO) declared that "the global is in tuberculosis emergency". And in2006, WHO launch a new DOTS-core TB control strategy, expecting to half the number of the TB cases in2015. China also classified TB as a key control disease. Recently, the spread of drug-resistant/multidrug-resistant TB has become the serious public health and social problem. And drug resistant (or multidrug-resistant) TB makes the general therapy method for TB ineffective, and also make TB become an incurable disease again. How to effectively reduce the drug-resistant TB cases and control its spread is currently a major problem.In this thesis, two drug-resistant tuberculosis dynamics models with exogenous re-infection is built according to the mechanism of the spread of tuberculosis and the modeling thought and method of epidemic dynamics. Considering the current research work has not suggest that how long the period of acquired immunity against TB is, our models in this thesis is with permanent and non-permanent immunity, respectively. By using the theory of differential equations, the asymptotic behaviors of the models is analyzed. The basic reproductive numbers of the two models are obtained, which determine whether the disease die out or remain endemic. The local asymptotic stability of disease-free equilibrium and endemic equilibrium is proved. And it is shown that there exist the backward bifurcation to our two models under certain conditions and the turn points are obtained. This result shows that whether or not the disease die out is not only depend on the basic reproductive number of models but also on the initial status (including the number of the susceptibles, the infectious and so on). In addition, the simulation is carried and thus the results of simulation not only verifies the correctness of the analysis results, but also quanti-tatively show that the spread pattern and laws of drug-resistant tuberculosis and the effect of the vaccination rate on the spread of TB. All results also reveal that the dynamics behavior of the drug-resistant tuberculosis dynamics models with ex- ogenous re-infection is not changed by the immunity period.