| Pests had more and more serious impact on agricultural production and caused huge economic losses.Therefore,how to effectively control pests has always been a very concerned issue for agricultural management departments.Common pest management methods include chemical control,biological control,physical control and Integrated Pest Management(IPM).Among them,chemical control is the most commonly used pest control strategy because of its convenient implementation and quick effect.However,pesticide resistance is a very difficult and challenging problem in pest management.On the one hand,people hope to control pests by spraying pesticides,on the other hand,the long-term and high-frequency use of the same type of pesticides will reduce the sensitivity and the efficacy of pests to this kind of pesticides,resulting in pesticide resistance.With the development of pesticide resistance,a paradoxical phenomenon often occurs whereby the stronger the control measures the more serious are subsequent outbreaks of pest populations.Therefore improper control measures against agricultural pests may lead to severe outbreaks rather than the desired control.In order to restrain the evolution of pesticide resistance and avoid such paradoxical effects happening,it is necessary to understand the mechanisms and dynamics of pest resistance development and ascertain the conditions for the occurrence of paradoxical result.In this paper,first,based on the genetic law of pest resistance genes,the frequency of pesticide use,etc.,the common resistance development equation of inheritance and induction is established.By discrete dynamical system,numerical analysis and other related theories and methods,we investigate the effects of the spraying times,the level of dominance of pesticide resistance allele and death rate of pesticide for homozygote susceptibles on frequence of resistance.Second,in order to introduce the pest resistance to pesticide model into pest control models,By impulse difference equations,hybrid dynamic systems and other related theoretical knowledge,we proposed the new methods of modeling pest populations with discrete generations and impulsive chemical control and developed a multi-scale system with equations combining description of pest populations and their genetic evolution.We carried out theoretical analysis of system.The threshold condition of pest eradication is given,and the relationship between threshold condition and pesticide resistance development was discussed in this paper.In order to deal with pesticide resistance develop and achieve the goal of pest management,in this paper,two switching strategies are proposed for different control purposes.The pesticide switching strategy based on threshold condition and economic injury level(EIL).The optimal pesticide switching time under different pesticide changing strategies was obtained by theoretical analysis.Finally,on the basis of the existing literature,a discrete predator-pest population dynamics model with multiple pesticide sprays in the pest generation is proposed.By the stability theory of difference equations,the existence and stability of extinction equilibrium point,boundary equilibrium point and nontrivial equilibrium point were analyzed,and the effects of spraying time and instantaneous killing rate of pesticide on pest control were discussed.We discussed the conditions of paradox of pest control strategy for the model and the effects of continuous incorrect spraying pesticide on pest outbreak.Two special models are simulated to analyze the effects of spraying time,efficiency of pesticide and spraying times in each generation on pest control strategy. |
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