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High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control

Author

Listed:
  • Feiping Xie

    (Jiangxi Provincial Key Laboratory of Pest and Disease Control of Featured Horticultural Plants, Gannan Normal University, Ganzhou 341000, China)

  • Youquan Luo

    (Jiangxi Provincial Key Laboratory of Pest and Disease Control of Featured Horticultural Plants, Gannan Normal University, Ganzhou 341000, China)

  • Yan Zhang

    (Jiangxi Provincial Key Laboratory of Pest and Disease Control of Featured Horticultural Plants, Gannan Normal University, Ganzhou 341000, China)

  • Shujing Gao

    (Jiangxi Provincial Key Laboratory of Pest and Disease Control of Featured Horticultural Plants, Gannan Normal University, Ganzhou 341000, China)

Abstract

This study develops a high-dimensional impulsive differential equation model to analyze Huanglongbing (HLB) transmission dynamics, incorporating seasonal fluctuations in vector psyllid populations and multi-pronged control measures: (1) periodic removal of infected/dead citrus trees to eliminate pathogen reservoirs and (2) non-uniform pesticide applications timed to disrupt psyllid life cycles. The model analytically derives the basic reproduction number ( R 0 ) and proves the existence of a unique disease-free periodic solution. Theoretical analysis reveals a threshold-dependent stability: when R 0 < 1 , the disease-free solution is globally asymptotically stable, ensuring pathogen extinction; when R 0 > 1 , the system becomes uniformly persistent, indicating endemic HLB. Numerical simulations validate these findings and demonstrate that integrated interventions, combining psyllid population control and removal of infected plants, can significantly suppress HLB spread. The results provide a mathematical framework for optimizing intervention timing and intensity, offering actionable strategies for citrus growers.

Suggested Citation

  • Feiping Xie & Youquan Luo & Yan Zhang & Shujing Gao, 2025. "High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control," Mathematics, MDPI, vol. 13(10), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1546-:d:1651620
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    References listed on IDEAS

    as
    1. Jianping Wang & Shujing Gao & Yueli Luo & Dehui Xie, 2014. "Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Jianping Wang & Shujing Gao & Yueli Luo & Dehui Xie, 2014. "Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, March.
    3. Yujiang Liu & Shujing Gao & Di Chen & Bing Liu, 2024. "Modeling the Transmission Dynamics and Optimal Control Strategy for Huanglongbing," Mathematics, MDPI, vol. 12(17), pages 1-23, August.
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