Abstract
A delayed predator-prey model with disease in the predator and stage structure for the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is studied. The existence of Hopf bifurcations at the disease-free equilibrium and the coexistence equilibrium are addressed, respectively. By using Lyapunov functions and LaSalle invariant principle, sufficient conditions are derived for the global stability of the trivial equilibrium, the predator-extinction equilibrium and the disease-free equilibrium, respectively. Further, sufficient conditions are derived for the global attractiveness of the coexistence equilibrium of the proposed system.
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