Note on the Stability Property of the Boundary Equilibria of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

We revisit the stability property of the boundary equilibria of a prey-predator model with a refuge-stage structure prey population. For the vanishing equilibrium point, our study shows that the conditions that ensure the local stability of the vanishing point are enough to ensure its global stability. The differential inequality theory is used to derive a set of easily verifiable requirements ensuring predator-free equilibrium’s global asymptotically stable behavior. Our results essentially improve some known results.