Persistence and spatial propagation of an impulsive integro-differential model with non-local pulse

In order to investigate the spatial distribution and evolution dynamics of populations exhibiting synchronized reproduction and two stage long-distance dispersal modes, in this paper we propose an impulsive integro-differential model with non-local pulse. Firstly, we establish the extinction and persistence dynamics on the bounded domain with Dirichlet boundary of non-local type. Secondly, we derive the existence and characterization of the spreading speed in the whole space as well as the consistency with the minimum wave speed of the traveling waves. Finally, numerical simulations are presented to study the effects of different dispersal patterns and dispersal allocation strategy on population persistence and spreading speed under a constant measure of total dispersal. Our results show that under the same overall variance, the non-local diffusion pattern has both higher steady-state density and greater spreading speed than the local diffusion pattern. Moreover, under the fixed total dispersal, the optimal state for both population persistence and spreading speed is usually achieved through a stage-concentrated dispersal strategy, where dispersal occurs in a single life stage and the other stages remain sedentary. Additionally, we numerically investigate the impact of overcompensation on threshold and propagation dynamics, serving as a complement to the theoretical results in the non-monotonic case. This work provides new insights into the understanding of non-local interactions in biology and ecology.