Stability Analysis Of A Few Tb Model

Vertical transmission and exogenous reinfection are exist in infectious diseases, so it isvery important for us to research. In this paper, we proved the global asymptotical stableresults of the disease-free equilibrium and the local asymptotical stable results of the endemicequilibrium by di?erential equation theorem. We proved the results of our model with thehelp of Maple and Matlab.In chapter1, importance and some work of research TB in our country and the overseasis introduced.In chapter2, an SEIT epidemic model with vertical transmission is considered. ByLyapunov function and LaSalle s invariant set theorem, we proved the global asymptoticalstable results of the disease-free equilibrium. By Descartes'Rule of Signs, we proved thelocal asymptotical stable results of the endemic equilibrium. We proved the results of ourmodel with the help of Maple and Matlab by numerical simulations.In chapter 3, an SEIT epidemic model that incorporates proportion recruitment andwith exogenous reinfection is considered. By Lyapunov function and LaSalle s invariant settheorem, we proved the global asymptotical stable results of the disease-free equilibrium.By Descartes'Rule of Signs, we proved the local asymptotical stable results of the endemicequilibrium. We proved the results of our model with the help of Maple and Matlab bynumerical simulations.