Dynamics behaviors of a stage-structured pest management model with time delay and impulsive effects

In this paper, we study a delayed stage-structured pest management model with periodic releasing infective pest, spraying pesticide and harvesting crop at three different fixed moments. By using impulsive-type comparison results, small-amplitude perturbation techniques, and the global attractivity of a one-order time-delay system, sufficient condition ensuring the global attractivity of the susceptible pest-eradication periodic solution is derived. Furthermore, the permanence of the model is also derived. An example and its numerical simulations are given to verify the effectiveness of the theoretical results.