A study of integrated pest management models with instantaneous and non-instantaneous impulse effects

Liping Wu; Zhongyi Xiang; Liping Wu; Zhongyi Xiang

doi:10.3934/mbe.2024136

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 2: 3063-3094. doi: 10.3934/mbe.2024136

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A study of integrated pest management models with instantaneous and non-instantaneous impulse effects

Liping Wu ¹,
Zhongyi Xiang ^{1,2
,
,}

1.
School of Mathematics and Statistics, Hubei Minzu University, Enshi 445000, Hubei, China
2.
Hubei Key Laboratory of Biologic Resources Protection and Utilization, Hubei Minzu University, Enshi 445000, Hubei, China

Received: 22 October 2023 Revised: 11 December 2023 Accepted: 09 January 2024 Published: 30 January 2024

The occurrence of pests and diseases during agricultural production affects the quality and quantity of agricultural products. It is important to evaluate the impact of various factors on pests to achieve optimal results of integrated pest management (IPM) during its implementation. In this paper, we considered the transient and non-transient effects of chemical control on pests and the effects on natural enemies at different times, and developed a corresponding pest control model. Detailed studies and comparisons were conducted for spraying pesticides either more or less frequently as compared to strategies for releasing natural enemies. The threshold conditions for global asymptotic stabilization of the pest extinction period solution was obtained. Using two-parameter and sensitivity analysis techniques, the parameters affecting the variation of the threshold were discussed. By comparing these two pest control strategies, we found the existence of optimal application and release frequencies. Finally, in order to control pests below the economic threshold level, the state-dependent pest model was numerically investigated. The results show that the presence or absence of chemical control of pests can depend on the values taken for the parameters in the model. Based on this information, pest control experts can make decisions about the best spraying time and the best release rate.
- integrated pest management,
- pesticide residue effects,
- sensitivity analysis,
- state-dependence pest model
Citation: Liping Wu, Zhongyi Xiang. A study of integrated pest management models with instantaneous and non-instantaneous impulse effects[J]. Mathematical Biosciences and Engineering, 2024, 21(2): 3063-3094. doi: 10.3934/mbe.2024136

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Abstract

The occurrence of pests and diseases during agricultural production affects the quality and quantity of agricultural products. It is important to evaluate the impact of various factors on pests to achieve optimal results of integrated pest management (IPM) during its implementation. In this paper, we considered the transient and non-transient effects of chemical control on pests and the effects on natural enemies at different times, and developed a corresponding pest control model. Detailed studies and comparisons were conducted for spraying pesticides either more or less frequently as compared to strategies for releasing natural enemies. The threshold conditions for global asymptotic stabilization of the pest extinction period solution was obtained. Using two-parameter and sensitivity analysis techniques, the parameters affecting the variation of the threshold were discussed. By comparing these two pest control strategies, we found the existence of optimal application and release frequencies. Finally, in order to control pests below the economic threshold level, the state-dependent pest model was numerically investigated. The results show that the presence or absence of chemical control of pests can depend on the values taken for the parameters in the model. Based on this information, pest control experts can make decisions about the best spraying time and the best release rate.

References

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