Models for determining the optimal switching time in chemical control of pest with pesticide resistance

Yanyun Li; Juhua Liang; Yanyun Li; Juhua Liang

doi:10.3934/mbe.2021026

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 471-494. doi: 10.3934/mbe.2021026

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Research article

Models for determining the optimal switching time in chemical control of pest with pesticide resistance

Yanyun Li ,
Juhua Liang ^,

School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China

Received: 17 September 2020 Accepted: 25 November 2020 Published: 09 December 2020

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.
- pesticide resistance,
- threshold condition,
- pesticide switching strategy,
- optimal switching time
Citation: Yanyun Li, Juhua Liang. Models for determining the optimal switching time in chemical control of pest with pesticide resistance[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 471-494. doi: 10.3934/mbe.2021026

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Abstract

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.

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