Study Of The Tuberculosis Dynamic Model With Endogenous Pathogenesis

Tuberculosis has become one of the chronic respiratory diseases concerted efforts of China and the world control, is one of the diseases included in the World Health Organization’s three key control. Sleep inside the pathogenesis of endogenous secondary pulmonary tuberculosis TB plays an important role in endogenous reinfection affect the spread of tuberculosis.This paper studies the dynamics model of tuberculosis within the contemplation of endogenous onset, and taking into account exogenous re-infection, prophylactic treatment and incomplete immunity and other factors. Analysis using the mathematical theory of dynamical systems theory and biological differential equations of the asymptotic behavior of the model. Through the qualitative and stability of the model analysis, it was found to have a rich dynamical form. We are established model of disease-free equilibrium and stability, the existence of endemic equilibrium and stability. When the basic reproductive number is greater than one, the disease is bound to pop, when disease-free equilibrium is unstable and there is no stable endemic equilibrium point, when the basic reproductive number is less than the time, the disease may be prevalent, this time in a range of memory in a local stable endemic equilibrium, disease-free equilibrium is locally stable also. Through the above research, prevention and control strategies for the epidemic of tuberculosis put forward relevant theoretical support.