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Dynamical analysis of plant disease models with cultural control strategies and economic thresholds

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

Abstract

In this paper plant disease models including impulsive cultural control strategies were developed and analyzed. The sufficient conditions under which the infected plant free periodic solution with fixed moments is globally stable are obtained. For the model with an economic threshold (ET) of infected plants, detailed investigations imply that the number of healthy plants either goes to extinction or tends to infinity, and the maximum value of infected plants is always less than the given ET. In order to prevent the healthy plant population going to extinction, we further propose a bi-threshold-value model, which has richer dynamical behavior including order 1-k or order k-1 periodic solutions with k≥1. Under certain parameter spaces, the infected plant free periodic solution is globally stable for the bi-threshold-value model. The modeling methods and analytical analysis presented can serve as an integrating measure to identify, evaluate and design appropriate plant disease control strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:5:p:894-921
    DOI: 10.1016/j.matcom.2009.10.004
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Li, Wenjie & Huang, Lihong & Guo, Zhenyuan & Ji, Jinchen, 2020. "Global dynamic behavior of a plant disease model with ratio dependent impulsive control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 120-139.
    2. Jiao, Xubin & Liu, Xiuxiang, 2024. "Rich dynamics of a delayed Filippov avian-only influenza model with two-thresholds policy," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Li, Qian & Xiao, Yanni, 2023. "Analysis of a hybrid SIR model combining the fixed-moments pulse interventions with susceptibles-triggered threshold policy," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    4. 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.

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