Study on integrated management model of <i>Bactericera gobica</i> Loginova combining resistance and stage structure

Mengge Zhao; Jinyan Wang; Mengge Zhao; Jinyan Wang

doi:10.3934/math.2025677

AIMS Mathematics

2025, Volume 10, Issue 7: 15088-15107. doi: 10.3934/math.2025677

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Research article

Study on integrated management model of Bactericera gobica Loginova combining resistance and stage structure

Mengge Zhao ,
Jinyan Wang ^,

School of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia 750021, China

Received: 23 April 2025 Revised: 12 June 2025 Accepted: 25 June 2025 Published: 01 July 2025
MSC : 34C60, 92D25, 92D40

In this paper, according to the biological characteristics of B. gobica, it was divided into psyllid nymphs and adults, considering the chemical control of B. gobica combined with biological control, according to the resistance of psyllid nymphs and adults to pesticides as well as the predatory role of the dominant natural enemies on it, and we established a model of integrated control of B. gobica combined with the resistance to pesticides and the structure of stage. We investigated the dynamical properties of the model developed, theoretically proved the consistent boundedness of the system, and demonstrated sufficient conditions for the existence and global attractiveness of the periodic extinction solution of B. gobica. The effect of resistance development on B. gobica population density was discussed numerically, and the integrated B. gobica management strategy was compared with a single control strategy (chemical or biological), the effect of the number of pesticide sprays on the development of resistance to B. gobica was investigated, as well as the timing of pesticide switching according to the threshold theory, and, finally, the effect of the rest of the key parameters on the extinction threshold of B. gobica was illustrated by the contour plots as well as by sensitivity analyses. The results showed that shortening the release of natural enemies and the pulse period of spraying, controlling the intrinsic growth rate of nymphs, selecting pesticides with lower killing effect on natural enemies, controlling the killing rate of pesticides on natural enemies, and increasing the number of natural enemies released can be of great help to the management of B. gobica.
- Bactericera gobica Loginova,
- pesticide resistance,
- integrated management,
- stage structured,
- sensitivity analysis
Citation: Mengge Zhao, Jinyan Wang. Study on integrated management model of Bactericera gobica Loginova combining resistance and stage structure[J]. AIMS Mathematics, 2025, 10(7): 15088-15107. doi: 10.3934/math.2025677

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Abstract

In this paper, according to the biological characteristics of B. gobica, it was divided into psyllid nymphs and adults, considering the chemical control of B. gobica combined with biological control, according to the resistance of psyllid nymphs and adults to pesticides as well as the predatory role of the dominant natural enemies on it, and we established a model of integrated control of B. gobica combined with the resistance to pesticides and the structure of stage. We investigated the dynamical properties of the model developed, theoretically proved the consistent boundedness of the system, and demonstrated sufficient conditions for the existence and global attractiveness of the periodic extinction solution of B. gobica. The effect of resistance development on B. gobica population density was discussed numerically, and the integrated B. gobica management strategy was compared with a single control strategy (chemical or biological), the effect of the number of pesticide sprays on the development of resistance to B. gobica was investigated, as well as the timing of pesticide switching according to the threshold theory, and, finally, the effect of the rest of the key parameters on the extinction threshold of B. gobica was illustrated by the contour plots as well as by sensitivity analyses. The results showed that shortening the release of natural enemies and the pulse period of spraying, controlling the intrinsic growth rate of nymphs, selecting pesticides with lower killing effect on natural enemies, controlling the killing rate of pesticides on natural enemies, and increasing the number of natural enemies released can be of great help to the management of B. gobica.

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