本文研究一类食饵具有阶段结构且捕食者染病的具有饱和发生率的捕食者-食饵模型的稳定性及其Hopf分支，讨论了由疾病的潜伏期引起的时滞对种群动力学性态的影响．通过分析特征方程，运用Hurwitz判定定理，讨论了该模型边界平衡点和正平衡点的局部稳定性，并得到了Hopf分支存在的充分条件；通过构造适当的Lyapunov泛函，运用LaSall不变集原理，讨论了该模型边界平衡点和正平衡点的全局稳定性，从而得到了疾病流行而最终形成地方病及消灭的充分条件．

In this paper, an eco-epidemiological predator-prey model with saturation incidence and stage structure for the prey is investigated. A time delay describing the latent period of the disease in this model is discussed. By analyzing the characteristic equations, the local stability of the boundary equilibria and the positive equilibrium is established, respectively. Moreover, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. By using Lyapunov functions and the 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 disease extinction and permanence of the model.