Threshold dynamics for a stage-structured model with non-local impulsive birth in a heterogeneous environment

In this paper, we examine the effect of spatial heterogeneity on a stage-structured population model with non-local impulsive birth. We begin by introducing a non-local impulsive reaction-advection-diffusion model with spatial heterogeneity to describe the stage-structured population dynamics, accounting for two distinct life cycle phases. Next, we convert this model into a discrete-time recursive system defined by a discrete map. By utilizing the theory of the asymptotic spectral radius of linearized operators, and verifying fundamental qualitative properties of the discrete map, we establish results on threshold dynamics of the recursive system, including the non-existence, existence, and global attractivity of non-trivial fixed points. Finally, numerical simulations are presented to illustrate the theoretical results and to assess the influence of key parameters, such as drift rates, mortality and reproduction functions, and dispersal kernels on population extinction or dispersal patterns.