Abstract
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.
Highlights
In the natural world, species does not exist alone
Based on the above discussions, we only prove the global attractivity of the equilibrium EK
Based on the above discussions, we only prove the global attractivity of the equilibrium E1
Summary
Species does not exist alone. While species spreads the disease, it competes with the other species for space or food, or it is predated by other species. By means of appropriate Lyapunov functions and limit theory, sufficient conditions are obtained for the global stability of the semitrivial boundary equilibria of model (1) We note that it is assumed in system (1) that each individual predator admits the same ability to feed on prey. Based on the above discussions, in this paper, we incorporate a stage structure for the predator and time delay due to the gestation of predator into the model (1). To this end, we study the following differential equations: βS (t) I (t) , dI (t). A brief discussion is given in Section 5 to conclude this work
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