Li Yanyun, Liang Juhua
School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China.
Math Biosci Eng. 2020 Dec 9;18(1):471-494. doi: 10.3934/mbe.2021026.
In this paper, we developed a novel resistant equation of pest to pesticide with externalinduced 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 conditionof 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.
在本文中，我们建立了一个具有外部诱导抗性和遗传抗性的害虫对杀虫剂的新型抗性方程，然后给出了该方程在抗性等位基因不同显性水平下的解析公式。进一步地，我们提出了具有离散世代和脉冲化学防治的害虫种群建模新方法，并开发了一个结合害虫种群及其遗传进化描述的多尺度系统。更详细地研究了害虫根除解的阈值条件，这使我们能够确定应切换不同类型杀虫剂的最佳时间。此外，我们还提供了一种以经济损害水平（EIL）为指导的杀虫剂切换方法，随后从害虫防治的角度讨论了一些生物学意义。
