Partial survival and extinction of a delayed predator–prey model with stage structure

In this paper, we revisit the non-persistent property of a stage-structured predator–prey system which was proposed by Ma et al. (2008) [Z.H. Ma, Z.Z. Li, S.F. Wang, T.Li, F.P. Zhang, Permanence of a predator–prey system with stage structure and time delay, Appl. Math. Comput. 201 (2008) pp. 65–71]. By applying the standard comparison theorem, some novel results concern with the extinction of the system and partial survival of the predator (prey) species, respectively, are obtained. One of the interesting finding is that for this system, the extinction of prey may not necessarily lead to extinction of predator.