In this paper, we assume that the pest population is divided into susceptible pests and infected pests, and only susceptible pests do harm to crops. Considering the two methods of spraying pesticides and releasing infected pests and natural enemies to control susceptible pests (the former is applied more frequently), and assuming that only susceptible pests develop resistance to pesticides, a pest control model with resistance development is established. By using the basic theory of impulsive differential systems and analytical methods, the sufficient condition for the global attractiveness of the susceptible pest eradication periodic solution is given. Combined with numerical simulations, the effects of spraying frequency of pesticides on critical threshold conditions for eradicating susceptible pests are discussed. The results confirm that it is not that the more frequently the pesticides are sprayed, the better the result of the pest control is. Two control strategies for eradicating susceptible pests are proposed: switching pesticides and releasing natural enemies elastically. Finally, the parameters in the critical threshold are analyzed from the following two aspects: (1) The key factors affecting pest control are determined by parameter sensitivity analyses. The results indicate that the correlation of the critical threshold concerning the killing efficiency rate and the decay rate of pesticides to susceptible pests varies due to the resistance development of susceptible pests. (2) Three-dimensional graphs and contours of susceptible pest eradication critical threshold with two parameters are simulated, and the effects of the main parameters on the critical threshold are analyzed.

中文翻译：

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随着农药抗性的发展模拟害虫控制的效果

在本文中，我们假设害虫种群分为易感害虫和感染害虫，只有易感害虫才会对作物造成危害。综合考虑喷洒农药和释放感染害虫和天敌两种方法来防治易感害虫（前者应用较多），并假设只有易感害虫对农药产生抗性，建立具有抗性发展的病虫害防治模型。利用脉冲微分系统的基本理论和分析方法，给出了易感害虫根除周期解具有全局吸引力的充分条件。结合数值模拟，讨论了农药喷洒频率对根除敏感害虫临界阈值条件的影响。结果证实，并非农药喷洒次数越多，防治病虫害的效果就越好。提出了两种消灭易感害虫的控制策略：切换农药和弹性释放天敌。最后，从以下两个方面对临界阈值中的参数进行分析： (1) 通过参数敏感性分析确定影响害虫防治的关键因素。结果表明，农药对感病害虫的杀灭效率和衰减率临界阈值的相关性因感病害虫抗性发展而异。(2) 模拟具有两个参数的易感害虫消灭临界阈值的三维图形和等高线，