A mathematical model of flavescence dorée in grapevines by considering seasonality
This paper presents a mathematical model to describe the spread of flavescence dorée, a disease caused by the bacterium Candidatus Phytoplasma vitis, which is transmitted by the insect vector Scaphoideus titanus in grapevine crops. The key contribution of this work is the derivation of conditions un...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2024332 |
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| author | Fernando Huancas Aníbal Coronel Rodolfo Vidal Stefan Berres Humberto Brito |
| author_facet | Fernando Huancas Aníbal Coronel Rodolfo Vidal Stefan Berres Humberto Brito |
| author_sort | Fernando Huancas |
| collection | DOAJ |
| description | This paper presents a mathematical model to describe the spread of flavescence dorée, a disease caused by the bacterium Candidatus Phytoplasma vitis, which is transmitted by the insect vector Scaphoideus titanus in grapevine crops. The key contribution of this work is the derivation of conditions under which positive periodic solutions exist. These conditions are based on the assumption that key factors such as recruitment rates, disease transmission, and vector infectivity vary periodically, thus reflecting seasonal changes. The existence of these periodic solutions is proven using the degree theory, and numerical examples are provided to support the theoretical findings. This model aims to enhance the understanding of the epidemiological dynamics of flavescence dorée and contribute to developing better control strategies to manage the disease in grapevines. |
| format | Article |
| id | doaj-art-b0920161d5064bdab9d0c9d94dbb5626 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b0920161d5064bdab9d0c9d94dbb56262025-01-23T07:48:07ZengAIMS PressMathematical Biosciences and Engineering1551-00182024-11-0121117554758110.3934/mbe.2024332A mathematical model of flavescence dorée in grapevines by considering seasonalityFernando Huancas0Aníbal Coronel1Rodolfo Vidal2Stefan Berres3Humberto Brito4Departamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras No. 3360, Ññoa-Santiago 7750000, ChileGMA, Departamento de Ciencias Básicas-Centro de Ciencias Exactas CCE-UBB, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, ChileDepartamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras No. 3360, Ññoa-Santiago 7750000, ChileNúcleo de Investigación en Bioproductos y Materiales Avanzados (BioMA), Universidad Católica de Temuco, Temuco 4780002, ChileDepartamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras No. 3360, Ññoa-Santiago 7750000, ChileThis paper presents a mathematical model to describe the spread of flavescence dorée, a disease caused by the bacterium Candidatus Phytoplasma vitis, which is transmitted by the insect vector Scaphoideus titanus in grapevine crops. The key contribution of this work is the derivation of conditions under which positive periodic solutions exist. These conditions are based on the assumption that key factors such as recruitment rates, disease transmission, and vector infectivity vary periodically, thus reflecting seasonal changes. The existence of these periodic solutions is proven using the degree theory, and numerical examples are provided to support the theoretical findings. This model aims to enhance the understanding of the epidemiological dynamics of flavescence dorée and contribute to developing better control strategies to manage the disease in grapevines.https://www.aimspress.com/article/doi/10.3934/mbe.2024332mathematical modeling of plant diseasesperiodic solutions in differential equationsdisease management in vineyardsseasonal vector population modelsvector-borne plant diseases |
| spellingShingle | Fernando Huancas Aníbal Coronel Rodolfo Vidal Stefan Berres Humberto Brito A mathematical model of flavescence dorée in grapevines by considering seasonality Mathematical Biosciences and Engineering mathematical modeling of plant diseases periodic solutions in differential equations disease management in vineyards seasonal vector population models vector-borne plant diseases |
| title | A mathematical model of flavescence dorée in grapevines by considering seasonality |
| title_full | A mathematical model of flavescence dorée in grapevines by considering seasonality |
| title_fullStr | A mathematical model of flavescence dorée in grapevines by considering seasonality |
| title_full_unstemmed | A mathematical model of flavescence dorée in grapevines by considering seasonality |
| title_short | A mathematical model of flavescence dorée in grapevines by considering seasonality |
| title_sort | mathematical model of flavescence doree in grapevines by considering seasonality |
| topic | mathematical modeling of plant diseases periodic solutions in differential equations disease management in vineyards seasonal vector population models vector-borne plant diseases |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2024332 |
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