Abstract: In this paper, the stability and Hopf bifurcation of an eco-epidemiological model with a time delay and a stage structure is investigated. By analyzing the characteristic equations and applying Hurwitz criterion, the local stability of the boundary equilibria and the positive equilibrium are discussed, respectively. Moreover, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. By using Lyapunov functions and LaSalle's invariance principle, the global stability of the boundary equilibria and the positive equilibrium is addressed, respectively. Therefore, the sufficient conditions are given for the permanence and extinction of the model.

Key words: eco-epidemiological model, stage structure, time delay, stability, Hopf bifurcation