In this paper, we describe a hybrid dynamical model incorporating residual and delayed effects of pesticides and pest resistance to simulate the process of integrated pest management. It assumes that spraying pesticides is more frequently used than releasing natural enemies. The threshold condition for pest-eradication is given. Combined with numerical simulations, the effects of chemical control factors on the threshold are discussed. The results confirm that it is not that the more frequently the pesticides are sprayed and the stronger effects the pesticides have on pests, the smaller the threshold is. Further, we give three different control strategies, including switching pesticide strategy and strategy for releasing natural enemies elastically for the pest-eradication, and the state feedback strategy for controlling pests not exceeding the economic injury level (EIL). The results indicate that if the purpose is to prevent the density of pest population from increasing to the EIL, from an ecological and economic perspective, it is not that the more natural enemies are released, and the better results are obtained.

中文翻译：

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结合虫害抗性和不同控制策略的混合虫害管理模型分析

在本文中，我们描述了一种混合动力模型，该模型结合了农药的残留和延迟效应以及对害虫的抵抗力，以模拟害虫综合治理的过程。它假定喷洒农药比释放天敌更常用。给出了根除有害生物的阈值条件。结合数值模拟，讨论了化学控制因素对阈值的影响。结果证实，并不是说农药喷洒得越频繁，农药对害虫的影响越强，阈值就越小。此外，我们提供了三种不同的控制策略，包括转换农药策略和为消灭害虫而弹性释放天敌的策略，以及控制有害生物不超过经济损害水平（EIL）的国家反馈策略。结果表明，从生态和经济的角度来看，如果目的是防止有害生物种群的密度增加到EIL，则不是天敌释放的越多，取得的效果就越好。