Mathematical Analysis Of An Stage-structured Model For Tuberculosis Transmission Dynamics

Tuberculosis (TB) is one of the oldest infectious diseases which causes serious damage to the human health. Tuberculosis (TB) is a global public health problem. In this paper, using the method of dynamics, we set up a class of tuberculosis model with stage-structured. This model mainly research the spread of tuberculosis with stage-structured. Dynamic characters of the model are discussed in the paper. We also simulate the data.First of all, according to the characteristics of the tuberculosis (TB), we divide the crowd into minors and adults. According to the crowd in different disease states, we divide the crowd into four categories:the susceptibles(S), the lurkers(L), the in-fections(I) and the treatments(T). We set up a class of stage-structured tuberculosis model with constant input. The second, using the stability theorem of Lyapunov, we get the stability of the disease-free equilibrium. When RO is less than one, the disease-free equilibrium is globally asymptotically stable. Combined with the real-ity of TB cases, when the parameters meet certain conditions, the model exists a unique positive equilibrium point. Using the stability principle of Lyapunov and the invariant principle of LaSalle, When R0 is larger than one, the endemic equilibrium is globally asymptotically stable. Combining with data of the Chinese center for disease control, we simulate it. Finally, we summarize the full text and determine the goal of future research.