Dynamics of HLB Transmission: Integrating Saturated Removal and Vector Bias in Spatial/Non-Spatial Models
Huanglongbing (HLB), a globally devastating citrus disease, demands sophisticated mathematical modeling to decipher its complex transmission dynamics and inform optimized disease management protocols. This investigation develops an innovative compartmental framework that simultaneously incorporates...
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2025-06-01
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| author | Yang Liu Yirong Gao Fumin Zhang Shujing Gao |
| author_facet | Yang Liu Yirong Gao Fumin Zhang Shujing Gao |
| author_sort | Yang Liu |
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| description | Huanglongbing (HLB), a globally devastating citrus disease, demands sophisticated mathematical modeling to decipher its complex transmission dynamics and inform optimized disease management protocols. This investigation develops an innovative compartmental framework that simultaneously incorporates two critical factors in HLB epidemiology: saturated removal rates of infected citrus trees and behavioral bias in vector movement patterns. Our study delves into the dynamics of non-spatial systems by analyzing the basic reproduction numbers, equilibria, bifurcation phenomena, and the stability of these equilibria. Additionally, we explore the impact of spatial factors on system stability. Results indicate that when the basic reproduction number <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 may exhibit bistable behavior, while <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> leads to a unique stable equilibrium. Notably, vector bias significantly enhances the likelihood of forward bifurcation, and the delay in the removal of diseased trees increases the risk of backward bifurcation. However, reaction–diffusion processes do not alter the stability of the system’s equilibria, and the spatial system lacks complex dynamic properties. This research offers valuable insights into the mechanisms driving HLB transmission and provides a foundation for developing effective control strategies. |
| format | Article |
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| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
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| spelling | doaj-art-c3ece7bc51da4e539ecb49601cba6da42025-08-20T03:26:15ZengMDPI AGAxioms2075-16802025-06-0114643410.3390/axioms14060434Dynamics of HLB Transmission: Integrating Saturated Removal and Vector Bias in Spatial/Non-Spatial ModelsYang Liu0Yirong Gao1Fumin 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, ChinaHuanglongbing (HLB), a globally devastating citrus disease, demands sophisticated mathematical modeling to decipher its complex transmission dynamics and inform optimized disease management protocols. This investigation develops an innovative compartmental framework that simultaneously incorporates two critical factors in HLB epidemiology: saturated removal rates of infected citrus trees and behavioral bias in vector movement patterns. Our study delves into the dynamics of non-spatial systems by analyzing the basic reproduction numbers, equilibria, bifurcation phenomena, and the stability of these equilibria. Additionally, we explore the impact of spatial factors on system stability. Results indicate that when the basic reproduction number <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 may exhibit bistable behavior, while <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> leads to a unique stable equilibrium. Notably, vector bias significantly enhances the likelihood of forward bifurcation, and the delay in the removal of diseased trees increases the risk of backward bifurcation. However, reaction–diffusion processes do not alter the stability of the system’s equilibria, and the spatial system lacks complex dynamic properties. This research offers valuable insights into the mechanisms driving HLB transmission and provides a foundation for developing effective control strategies.https://www.mdpi.com/2075-1680/14/6/434Huanglongbing modelreaction–diffusionsaturation effectbiasbifurcation |
| spellingShingle | Yang Liu Yirong Gao Fumin Zhang Shujing Gao Dynamics of HLB Transmission: Integrating Saturated Removal and Vector Bias in Spatial/Non-Spatial Models Axioms Huanglongbing model reaction–diffusion saturation effect bias bifurcation |
| title | Dynamics of HLB Transmission: Integrating Saturated Removal and Vector Bias in Spatial/Non-Spatial Models |
| title_full | Dynamics of HLB Transmission: Integrating Saturated Removal and Vector Bias in Spatial/Non-Spatial Models |
| title_fullStr | Dynamics of HLB Transmission: Integrating Saturated Removal and Vector Bias in Spatial/Non-Spatial Models |
| title_full_unstemmed | Dynamics of HLB Transmission: Integrating Saturated Removal and Vector Bias in Spatial/Non-Spatial Models |
| title_short | Dynamics of HLB Transmission: Integrating Saturated Removal and Vector Bias in Spatial/Non-Spatial Models |
| title_sort | dynamics of hlb transmission integrating saturated removal and vector bias in spatial non spatial models |
| topic | Huanglongbing model reaction–diffusion saturation effect bias bifurcation |
| url | https://www.mdpi.com/2075-1680/14/6/434 |
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