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Multiple attractors of host–parasitoid models with integrated pest management strategies: Eradication, persistence and outbreak

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  • Tang, Sanyi
  • Xiao, Yanni
  • Cheke, Robert A.

Abstract

Host–parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host–parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host’s intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic.

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  • Tang, Sanyi & Xiao, Yanni & Cheke, Robert A., 2008. "Multiple attractors of host–parasitoid models with integrated pest management strategies: Eradication, persistence and outbreak," Theoretical Population Biology, Elsevier, vol. 73(2), pages 181-197.
    • Handle: RePEc:eee:thpobi:v:73:y:2008:i:2:p:181-197
    DOI: 10.1016/j.tpb.2007.12.001
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    References listed on IDEAS

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    1. J. C. Headley, 1968. "Estimating the Productivity of Agricultural Pesticides," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 50(1), pages 13-23.
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    Cited by:

    1. Tang, Guangyao & Qin, Wenjie & Tang, Sanyi, 2014. "Complex dynamics and switching transients in periodically forced Filippov prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 13-23.
    2. Xiang, Zhongyi & Tang, Sanyi & Xiang, Changcheng & Wu, Jianhong, 2015. "On impulsive pest control using integrated intervention strategies," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 930-946.
    3. Yang, Jin & Tang, Sanyi & Tan, Yuanshun, 2016. "Complex dynamics and bifurcation analysis of host–parasitoid models with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 522-532.
    4. Wang, Xia & Xu, Zihui & Tang, Sanyi & Cheke, Robert A., 2017. "Cumulative effects of incorrect use of pesticides can lead to catastrophic outbreaks of pests," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 7-19.
    5. Liang, Juhua & Tang, Sanyi & Cheke, Robert A., 2016. "Pure Bt-crop and mixed seed sowing strategies for optimal economic profit in the face of pest resistance to pesticides and Bt-corn," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 6-21.
    6. Lirong Liu & Changcheng Xiang & Guangyao Tang & Yuan Fu, 2019. "Sliding Dynamics of a Filippov Forest-Pest Model with Threshold Policy Control," Complexity, Hindawi, vol. 2019, pages 1-17, November.
    7. Tang, Sanyi & Xiao, Yanni & Cheke, Robert A., 2010. "Dynamical analysis of plant disease models with cultural control strategies and economic thresholds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 894-921.
    8. Zhao, Tingting & Xiao, Yanni, 2015. "Plant disease models with nonlinear impulsive cultural control strategies for vegetatively propagated plants," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 61-91.
    9. Jiménez, María Fernanda & Blé, Gamaliel & Falconi, Manuel, 2022. "A biocontrol agent as a commensal in a plant-pest interaction," Ecological Modelling, Elsevier, vol. 468(C).
    10. Peipei Wang & Wenjie Qin & Guangyao Tang, 2019. "Modelling and Analysis of a Host-Parasitoid Impulsive Ecosystem under Resource Limitation," Complexity, Hindawi, vol. 2019, pages 1-12, January.
    11. Cheng, Huidong & Li, Wei & Zhang, Tonghua, 2024. "Complex dynamic analysis of a big fish-small fish system by using the Poincaré map," Applied Mathematics and Computation, Elsevier, vol. 482(C).

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