Properties Analysis Of Two Tuberculosis Dynamics Models

Tuberculosis, commonly known as "white plague", also known as the "consump-tion", is a kind of non-viral chronic infectious disease caused by Mycobactcrium tuberculosis. There are many different kinds of tuberculosis (TB), including such as pulmonary tuberculosis, liver TB, intestinal tuberculosis, pulmonary tuberculosis is one of the most common TB, occupy the vast majority of TB. TB has the charac-teristic of strong infectious, difficult to cure, easy to relapse and so on. Since we have found the Mycobacterium tuberculosis, there are millions more patients died of tuberculosis, so it causes people’s widespread attention to tuberculosis. So we are very necessary to use the method of epidemic dynamics to study the key factors which influence the prevalence of tuberculosis, forecast the development trend of tuberculosis, and prevent the disease by the best methods. According to the actu-al transmission characteristics of TB, considering various factors, we establish two kinds of TB model by using the method of epidemic dynamics.The time of individuals to show symptoms after infected with TB bacilli is different, that is, the disease has acute and chronic two phase. In chapter three, we take into account this factor and study a model with fast and slow Tuberculosis. Firstly, by using the Lyapunov stability theory, LaSalle’s invariant set theory, we discuss the global asymptotic stability of disease-free equilibrium and obtain that the disease will die if R0< 1; Secondly, we prove the local stability of endemic equilibrium by using the Routh-Hurwitz criterion; Finally, we perform the numerical simulation and parameter sensitivity analysis.In chapter four, a TB dynamic model with isolation is formulated and studied. Firstly, we discuss the conditions for the existence of equilibriums. Then, we use the theories and methods of the stability to prove the local asymptotic stability and the global asymptotic stability of each equilibrium point. Finally, we use the matlab to verify the theoretical results obtained. At the same time, by the numerical simulation, we also get the conclusion that the number of the infectious is decreased with the increase of isolation rate. Combined with the results of the numerical simulation. we discuss the effective measures to control TB.