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Modeling the Transmission Dynamics and Optimal Control Strategy for Huanglongbing

Author

Listed:
  • Yujiang Liu

    (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)

  • Di Chen

    (Jiangxi Institute of Applied Science and Technology, Nanchang 330100, China)

  • Bing Liu

    (School of Mathematics, Anshan Normal University, Anshan 114007, China)

Abstract

Huanglongbing (HLB), also known as citrus greening disease, represents a severe and imminent threat to the global citrus industry. With no complete cure currently available, effective control strategies are crucial. This article presents a transmission model of HLB, both with and without nutrient injection, to explore methods for controlling disease spread. By calculating the basic reproduction number ( R 0 ) and analyzing threshold dynamics, we demonstrate that the system remains globally stable when R 0 < 1 , but persists when R 0 > 1 . Sensitivity analyses reveal factors that significantly impact HLB spread on both global and local scales. We also propose a comprehensive optimal control model using the pontryagin minimum principle and validate its feasibility through numerical simulations. Results show that while removing infected trees and spraying insecticides can significantly reduce disease spread, a combination of measures, including the production of disease-free budwood and nursery trees, nutrient solution injection, removal of infected trees, and insecticide application, provides superior control and meets the desired control targets. These findings offer valuable insights for policymakers in understanding and managing HLB outbreaks.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2648-:d:1464303
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    References listed on IDEAS

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    1. Pang, Liuyong & Ruan, Shigui & Liu, Sanhong & Zhao, Zhong & Zhang, Xinan, 2015. "Transmission dynamics and optimal control of measles epidemics," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 131-147.
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