一类具有时滞的SIRS的传染病模型的稳定性分析和hopf分支

SIRS epidemic model with time delay is discussed by analyzing the characteristic equation, the local stability of the endemic equilibrium of the system is discussed and the existence of a Hopf bifurcation at the positive equilibrium is established. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each feasible equilibria of the model is discussed. When the time delay is disappeared, global exponential asymptotically stability of the disease-free equilibrium is discussed.