Study On The Dynamics Of Tuberculosis Models

This paper mainly studied the dynamics of two tuberculosis models, one is an SEIRV tuberculosis model with BCG vaccination, the other is a traditional tuberculosis model with migrant population. The dissertation includes five chapters.In chapter one, we introduce the development history and current research of the dynamics of tuberculosis models, the research basis and the main content of this paper.In chapter two, we introduce the relevant knowledge of the dynamics of tuberculosis models and the relevant stability theory.In chapter three, the dynamics of an SEIRV tuberculosis model with BCG vaccination is investigated, and the basic reproduction number0 R is obtained. By the Hurwitz criterion and the Liapunov function, the global stability of the disease-free equilibrium was obtained. The existence and uniqueness of the endemic equilibrium was given. The permanence of the model was proved by the permanence theory.In chapter four, we formulated one tuberculosis model with migrant population. By using the Liapunov stability theory and La Salle’s invariant set theory, we discuss the stability of the disease free equilibrium and the existence of the endemic equilibrium, which determined by the threshold condition. When the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable, and when the basic reproduction number is great than unity, the existence and uniqueness of the endemic and the bounded equilibrium was given.In chapter five, we summarize the main research results of the dynamics of tuberculosis models in this dissertation and point out some issues which need further research.