Analysis Of Tuberculosis Inection Dynamic Models

In this thesis, we mainly study the incubation period for patients with tuberculosis and tu-berculosis relapse of these two problems, and establish SEIR tuberculosis transmission model with general disease incidence and time delay, as well as tuberculosis transmission dynamic-s model with time delay recurrence respectively. Also we study the dynamic properties with models and biological meanings. This thesis is composed of four chapters as follows:In Chapter 1, we systematically introduce the research of tuberculosis and the epidemic of tuberculosis in China, and the current research status of the tuberculosis models at home and abroad. Meanwhile the major content of this paper as well as some preliminaries are briefly stated.In Chapter 2, a tuberculosis transmission model is studied that incorporates the distributed delays and general disease incidences. We study the global stability analysis of this model. By using the next generation matrix method, we get the the basic reproduction number of the model. By constructing of Lyapunov functionals, it is shown that the global stability of the model is completely determined by the basic reproductive number, when the basic reproduction number is equal to or less than one, the infection-free equilibrium is globally asymptotically stable is proved, and that the disease becomes endemic when the basic reproduction number is larger than one.In Chapter 3, we propose the tuberculosis transmission model which incorporates the dis-tributed delays, relapse distribution and general incidences, and obtain two main relevant results. Firstly, by constructing a Lyapunov functionals, we get the local and global asymptotic stability of disease-free equilibrium, and obtain the disease has been eradicated if R0<1; Secondly, we prove the local stability of endemic equilibrium, also we obtain the sufficient conditions of global asymptotic stability by taking advantage of the Lyapunov functionals.In the last chapter, the main contents of this thesis are briefly summarized and some worth-while future works related to our results are put forward.