Pulse Control Theory Applied Research In Integrated Pest Management

Pest control plays an important role in agriculture. Mathematical models of di?erentialequations play an important role in describing pest population dynamic behavior. Especially,impulsive di?erential equations describe pest population dynamic models, which is morereasonable and precise on re?ecting all kinds of change orderliness, since the reproductionand damager of pests, human control behavior are almost periodical in the natural world.In this paper, we investigate and study the dynamic behaviors of three classes ofeco-epidemiological models by means of the theory and method of impulsive di?erentialequations concerning integrated pest management strategy, i.e., periodic releasing infec-tive pests (or natural enemy) and spraying pesticide at di?erent fixed time. They arean eco-epidemiological model with impulsive e?ect and nonlinear incidence rate, an eco-epidemiological model with impulsive e?ect and Ivlev functional response and a class ofprey-dependent eco-epidemiological model with impulsive e?ect, respectively.We prove that all solutions of the investigated system are uniformly ultimately boundedrespectively. By applying the Floquet theorem and comparison theorem, we prove that thereexists a globally asymptotically stable susceptible pest-eradication periodic solution when theimpulsive period is less than some critical value. Otherwise, the system can be permanent.Finally, to substantiate our analytical results, numerical simulations are used to investigatedynamical behaviors including the existence of periodic solution, permanence, extinctionand stability. Mathematically, the theoretical evidence of the controlling pests using theintegrated pest management strategy in agriculture is given by the obtained results.