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Stability and bifurcation analysis on an ecoepidemiological model with stage structure and time delay. (English) Zbl 1474.34512

Summary: An ecoepidemiological predator-prey model with stage structure for the predator and time delay due to the gestation of the predator is investigated. The effects of a prey refuge with disease in the prey population are concerned. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is discussed. Further, it is proved that the model undergoes a Hopf bifurcation at the positive equilibrium. By means of appropriate Lyapunov functions and LaSalle’s invariance principle, sufficient conditions are obtained for the global stability of the semitrivial boundary equilibria. By using an iteration technique, sufficient conditions are derived for the global attractiveness of the positive equilibrium.

MSC:

34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D30 Epidemiology
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References:

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