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Pest Control Model With Delayed Stage Structure for Pest and Nonlinearly Impulsive Releasing Predator

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  • Guiyu Wu
  • Jianjun Jiao
  • Xiangjun Dai

Abstract

Considering the low cost and minimal environmental impact, nonlinear impulsive biological control strategies are more consistent with the pest management. From this basic standpoint, we formulate a pest control model incorporating delayed stage structure for the pest population and nonlinear impulsive release of natural enemies, and then conduct a mathematical and ecological investigation. By comparison theorem of impulsive differential equations and some analysis methods of delay differential equations, the sufficient condition for the global attractivity of the pest‐extinction periodic solution is obtained, and the threshold condition for the permanence of the system is given as well. Our mathematical results show that the maturation time delay for the pest and the nonlinear impulsive release of natural enemies play significant roles in governing the dynamics of the proposed system and the result of biological pest control. Model analysis also demonstrates that, when the mature pest populations are uniformly persistent, they can further be kept under the economic threshold level by controlling the crucial ecological parameters. Finally, our findings are illustrated through some numerical simulations.

Suggested Citation

  • Guiyu Wu & Jianjun Jiao & Xiangjun Dai, 2025. "Pest Control Model With Delayed Stage Structure for Pest and Nonlinearly Impulsive Releasing Predator," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:5547439
    DOI: 10.1155/jom/5547439
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    References listed on IDEAS

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    1. Jiao, Jianjun & Chen, Lansun & Cai, Shaohong, 2009. "A delayed stage-structured Holling II predator–prey model with mutual interference and impulsive perturbations on predator," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1946-1955.
    2. Kaikai Fang & Xiaomei Yi & Wei Dai & Hui Gao & Linkui Cao, 2019. "Effects of Integrated Rice-Frog Farming on Paddy Field Greenhouse Gas Emissions," IJERPH, MDPI, vol. 16(11), pages 1-17, May.
    3. Sun, Kaibiao & Zhang, Tonghua & Tian, Yuan, 2017. "Dynamics analysis and control optimization of a pest management predator–prey model with an integrated control strategy," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 253-271.
    4. Ghosh, Bapan & Grognard, Frédéric & Mailleret, Ludovic, 2015. "Natural enemies deployment in patchy environments for augmentative biological control," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 982-999.
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