High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control
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 pat...
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MDPI AG
2025-05-01
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| author | Feiping Xie Youquan Luo Yan Zhang Shujing Gao |
| author_facet | Feiping Xie Youquan Luo Yan Zhang Shujing Gao |
| author_sort | Feiping Xie |
| collection | DOAJ |
| description | 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula>) and proves the existence of a unique disease-free periodic solution. Theoretical analysis reveals a threshold-dependent stability: when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, the disease-free solution is globally asymptotically stable, ensuring pathogen extinction; when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, 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. |
| format | Article |
| id | doaj-art-6450c56cde2a4df38ddfdd5227a1c3ab |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-6450c56cde2a4df38ddfdd5227a1c3ab2025-08-20T03:47:57ZengMDPI AGMathematics2227-73902025-05-011310154610.3390/math13101546High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive ControlFeiping Xie0Youquan Luo1Yan Zhang2Shujing Gao3Jiangxi Provincial Key Laboratory of Pest and Disease Control of Featured Horticultural Plants, Gannan Normal University, Ganzhou 341000, ChinaJiangxi Provincial Key Laboratory of Pest and Disease Control of Featured Horticultural Plants, Gannan Normal University, Ganzhou 341000, ChinaJiangxi Provincial Key Laboratory of Pest and Disease Control of Featured Horticultural Plants, Gannan Normal University, Ganzhou 341000, ChinaJiangxi Provincial Key Laboratory of Pest and Disease Control of Featured Horticultural Plants, Gannan Normal University, Ganzhou 341000, ChinaThis 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula>) and proves the existence of a unique disease-free periodic solution. Theoretical analysis reveals a threshold-dependent stability: when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, the disease-free solution is globally asymptotically stable, ensuring pathogen extinction; when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, 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.https://www.mdpi.com/2227-7390/13/10/1546Huanglongbing modelbasic reproduction numbertime-varying impulseglobal asymptotic stabilityuniform persistence |
| spellingShingle | Feiping Xie Youquan Luo Yan Zhang Shujing Gao High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control Mathematics Huanglongbing model basic reproduction number time-varying impulse global asymptotic stability uniform persistence |
| title | High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control |
| title_full | High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control |
| title_fullStr | High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control |
| title_full_unstemmed | High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control |
| title_short | High-Dimensional Modeling of Huanglongbing Dynamics with Time-Varying Impulsive Control |
| title_sort | high dimensional modeling of huanglongbing dynamics with time varying impulsive control |
| topic | Huanglongbing model basic reproduction number time-varying impulse global asymptotic stability uniform persistence |
| url | https://www.mdpi.com/2227-7390/13/10/1546 |
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