In this paper, we developed a novel resistant equation of pest to pesticide with external~induced resistance and genetic resistance, and then the analytical formula of this equation under different level of dominance of resistance allele is given. Further, we proposed the new methods of modelling pest populations with discrete generations and impulsive chemical control and developed a multi-scale system combining descriptions of pest populations and their genetic evolution. The threshold condition~of pest eradication solution was investigated in more detail, which allows us to address the optimal time when different types of pesticides should be switched. Moreover, we also provided a pesticide switching method guided by the economic injury level (EIL), and then some biological implications have been discussed in terms of pest control.
Keywords: optimal switching time; pesticide resistance; pesticide switching strategy; threshold condition.