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

Feiping Xie, Youquan Luo, Yan Zhang and Shujing Gao ()
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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

Mathematics, 2025, vol. 13, issue 10, 1-22

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.

Keywords: Huanglongbing model; basic reproduction number; time-varying impulse; global asymptotic stability; uniform persistence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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