Abstract
A stage-structured predator–prey model with a transmissible disease spreading in the predator population and a time delay due to the gestation of the predator is formulated and analyzed. By analyzing corresponding characteristic equations, the local stability of each feasible equilibria and the existence of Hopf bifurcations at the disease-free equilibrium and the coexistence equilibrium are addressed, respectively. By using Lyapunov functions and the 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. Numerical simulations are carried out to support the theoretical analysis.
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