Tuberculosis (tb) Dynamic Model Of Stability Analysis

Epidemic dynamics is to study disease spread, predict the trends of the disease, fnd outthe key factors in the process of the spread, and prevent the disease by the best methods.TB is a chronic infectious diseases and is one of the oldest diseases in the human recorded.Tuberculosis patients in China accounted for a quarter of the world. The time of individualsto show symptoms after infected with TB bacilli is diferent. And the treatment time isvery diferent, that is, the disease has acute and chronic two phases. The ability to transmitvirus in diferent stages of infection is diferent. In this paper, we take into account diferentfactors and create several types of TB model.In chapter 2, a model with fast and slow Tuberculosis is studied, that is, consideringthe disease has acute and chronic phase of two. First, we discuss the local and globalasymptotic stability of disease-free equilibrium and obtain the disease has been eradicated ifR₀< 1; Secondly, we prove the local stability of endemic equilibrium, and use the Lyapunovfunction obtained sufcient conditions of global stability; Thirdly, we perform the numericalsimulation and parameter sensitivity analysis; Finally, according to this theory methods toexpand the study of HFMD in China.In chapter 3, we averagely divide the incubation period into n stages and formulate aSLIT TB model with staged progression based on the second chapter. Using the method ofnext-generation matrix, we obtain the basic reproductive number. The global stability ofthe equilibrium are proved by constructing appropriate Lyapunov function.In chapter 4, the model also divide the sick period into n stages based on the thirdchapter. First, we study the basic reproductive number of the model; Second, to prove theexistence and uniqueness of the equilibrium by using the matrix theory; Finally, we provethe global stability of the equilibrium by constructing appropriate Lyapunov function.