Based Pest Control Pulse Delay Differential Model

Pest control plays an important role in agriculture. The use of di?erential equationmodel to control pest has become an important research direction in the field of mathematics.Delay impulsive equations, which consider the e?ects of both the present state and the passedstate on the behavior of dynamical system, is more suitable to describe the populationdynamical system.In this paper, according to the study of systems both at home and abroad in recent years,we carefully studied the following three dynamic models which are established to considerseveral problems in pest management by means of the theory and method of delayed functiondi?erential equation and impulsive di?erential equations.First, in order to control the pest, we explore the control strategy of delivering ofnatural enemies or infected pests, and consider the stage-structure and time delay for thepest, finally, population dynamics model and epidemiological model were set up. By usingcomparative theorem of impulsive di?erential equation and delay di?erential equation basictheory, su?cient conditions which guarantee the global attraction of pest-extinction periodicsolution and permanence of the system are obtained, we also prove that all solutions of thesystem are uniformly ultimately bounded.Second, according to the idea of integrated pest management, we consider a pest man-agement ecosystem epidemic model with disease in the pest and stage structure for its naturepredator, simultaneously, the susceptible insects is harvested impulsively. By using compar-ative theorem of impulsive di?erential equation and delay di?erential equation basic theory,su?cient conditions which guarantee the global attraction of predator and infective pest-eradiation periodic solution and permanence of the system are obtained. We also prove thatall solutions of the system are uniformly ultimately bounded. Our results provide reliabletactical basis for the practical pest management.