Stability results for a size-structured population model with delayed birth process

In this paper, we discuss the qualitative behavior of an age/size-structured population equation with delay in the birth process. The linearization about stationary solutions is analyzed by semigroup and spectral methods. In particular, the spectrally determined growth property of the linearized semigroup is derived from its long-term regularity. These analytical results allow us to derive linearized stability and instability results under some conditions. The principal stability criterions are given in terms of a modified net reproduction rate. Finally, two examples are presented and simulated to illustrated the obtained conclusions.