Analysis of a hybrid pest management model incorporating pest resistance and different control strategies

Bing Liu; Gang Hu; Baolin Kang; Xin Huang; Bing Liu; Gang Hu; Baolin Kang; Xin Huang

doi:10.3934/mbe.2020241

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 4364-4383. doi: 10.3934/mbe.2020241

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Research article

Analysis of a hybrid pest management model incorporating pest resistance and different control strategies

1.
School of Mathematics and Information Science, Anshan Normal University, Anshan 114007, China
2.
College of Automation, Harbin Engineering University, Harbin 150001, China

Received: 08 April 2020 Accepted: 16 June 2020 Published: 22 June 2020

In this paper, we describe a hybrid dynamical model incorporating residual and delayed effects of pesticides and pest resistance to simulate the process of integrated pest management. It assumes that spraying pesticides is more frequently used than releasing natural enemies. The threshold condition for pest-eradication is given. Combined with numerical simulations, the effects of chemical control factors on the threshold are discussed. The results confirm that it is not that the more frequently the pesticides are sprayed and the stronger effects the pesticides have on pests, the smaller the threshold is. Further, we give three different control strategies, including switching pesticide strategy and strategy for releasing natural enemies elastically for the pest-eradication, and the state feedback strategy for controlling pests not exceeding the economic injury level (EIL). The results indicate that if the purpose is to prevent the density of pest population from increasing to the EIL, from an ecological and economic perspective, it is not that the more natural enemies are released, and the better results are obtained.
- hybrid pest management model,
- resistance,
- switching pesticide,
- releasing natural enemies elastically,
- state feedback control
Citation: Bing Liu, Gang Hu, Baolin Kang, Xin Huang. Analysis of a hybrid pest management model incorporating pest resistance and different control strategies[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4364-4383. doi: 10.3934/mbe.2020241

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Abstract

In this paper, we describe a hybrid dynamical model incorporating residual and delayed effects of pesticides and pest resistance to simulate the process of integrated pest management. It assumes that spraying pesticides is more frequently used than releasing natural enemies. The threshold condition for pest-eradication is given. Combined with numerical simulations, the effects of chemical control factors on the threshold are discussed. The results confirm that it is not that the more frequently the pesticides are sprayed and the stronger effects the pesticides have on pests, the smaller the threshold is. Further, we give three different control strategies, including switching pesticide strategy and strategy for releasing natural enemies elastically for the pest-eradication, and the state feedback strategy for controlling pests not exceeding the economic injury level (EIL). The results indicate that if the purpose is to prevent the density of pest population from increasing to the EIL, from an ecological and economic perspective, it is not that the more natural enemies are released, and the better results are obtained.

References

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