Dynamic Analysis and Optimal Control of the Spread of Tungro Virus Disease in Rice Plants Considering Refugia Planting and Pesticide Application
One of the main obstacles in rice cultivation is tungro disease, caused by <i>Rice Tungro Spherical Virus</i> (RTSV) and <i>Rice Tungro Bacilliform Virus</i> (RTBV), which are transmitted by green leafhopper vectors (<i>Nephotettix virescens</i>). This disease can...
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2024-12-01
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| author | Rika Amelia Nursanti Anggriani Asep K. Supriatna Noor Istifadah |
| author_facet | Rika Amelia Nursanti Anggriani Asep K. Supriatna Noor Istifadah |
| author_sort | Rika Amelia |
| collection | DOAJ |
| description | One of the main obstacles in rice cultivation is tungro disease, caused by <i>Rice Tungro Spherical Virus</i> (RTSV) and <i>Rice Tungro Bacilliform Virus</i> (RTBV), which are transmitted by green leafhopper vectors (<i>Nephotettix virescens</i>). This disease can be controlled by using pesticides and refugia plants. Excessive use of pesticides can have negative impacts and high costs, so it is necessary to control the use of pesticides. In this study, a mathematical model of the spread of tungro virus disease in rice plants was developed by considering the characteristics of the virus, the presence of green leafhoppers and natural enemies, refugia planting, and pesticide use. From this model, dynamic and sensitivity analyses were carried out, and the optimal control theory was searched using the Pontryagin minimum principle. The analysis results showed three equilibriums: two non-endemic equilibriums (when plant and vector populations exist and when plant, vector, and natural enemy populations exist) and one endemic equilibrium. The non-endemic equilibrium will be asymptotically stable locally if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. At the same time, the parameters that greatly influence the spread of this disease are parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>μ</mi><mo>,</mo><mo> </mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi></mrow></semantics></math></inline-formula> for local sensitivity analysis and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>,</mo><mo> </mo><mi>a</mi><mo>,</mo><mo> </mo><mi>β</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>ϕ</mi><mo>,</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> for global sensitivity analysis. The results of the numerical simulation show that control using combined control is more effective in reducing the intensity of the spread of tungro disease in rice plants than control in the form of planting refugia plants as a source of food for natural enemies. The use of pesticides is sufficient for only four days, so the costs incurred are quite effective in controlling the spread of this disease. |
| format | Article |
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| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-b5366e1c35e247969c43fef84a890fdc2025-08-20T02:43:49ZengMDPI AGMathematics2227-73902024-12-011224397910.3390/math12243979Dynamic Analysis and Optimal Control of the Spread of Tungro Virus Disease in Rice Plants Considering Refugia Planting and Pesticide ApplicationRika Amelia0Nursanti Anggriani1Asep K. Supriatna2Noor Istifadah3Post Doctoral Program, Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, Bandung 45363, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, Bandung 45363, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, Bandung 45363, IndonesiaDepartment of Plant Pathology, Faculty of Agriculture, Universitas Padjadjaran, Bandung 45363, IndonesiaOne of the main obstacles in rice cultivation is tungro disease, caused by <i>Rice Tungro Spherical Virus</i> (RTSV) and <i>Rice Tungro Bacilliform Virus</i> (RTBV), which are transmitted by green leafhopper vectors (<i>Nephotettix virescens</i>). This disease can be controlled by using pesticides and refugia plants. Excessive use of pesticides can have negative impacts and high costs, so it is necessary to control the use of pesticides. In this study, a mathematical model of the spread of tungro virus disease in rice plants was developed by considering the characteristics of the virus, the presence of green leafhoppers and natural enemies, refugia planting, and pesticide use. From this model, dynamic and sensitivity analyses were carried out, and the optimal control theory was searched using the Pontryagin minimum principle. The analysis results showed three equilibriums: two non-endemic equilibriums (when plant and vector populations exist and when plant, vector, and natural enemy populations exist) and one endemic equilibrium. The non-endemic equilibrium will be asymptotically stable locally if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. At the same time, the parameters that greatly influence the spread of this disease are parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>μ</mi><mo>,</mo><mo> </mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi></mrow></semantics></math></inline-formula> for local sensitivity analysis and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>,</mo><mo> </mo><mi>a</mi><mo>,</mo><mo> </mo><mi>β</mi><mo>,</mo><mo> </mo><mi>b</mi><mo>,</mo><mo> </mo><mi>ϕ</mi><mo>,</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> for global sensitivity analysis. The results of the numerical simulation show that control using combined control is more effective in reducing the intensity of the spread of tungro disease in rice plants than control in the form of planting refugia plants as a source of food for natural enemies. The use of pesticides is sufficient for only four days, so the costs incurred are quite effective in controlling the spread of this disease.https://www.mdpi.com/2227-7390/12/24/3979dynamic analysissensitivity analysisoptimal controlrefugia cropspesticide |
| spellingShingle | Rika Amelia Nursanti Anggriani Asep K. Supriatna Noor Istifadah Dynamic Analysis and Optimal Control of the Spread of Tungro Virus Disease in Rice Plants Considering Refugia Planting and Pesticide Application Mathematics dynamic analysis sensitivity analysis optimal control refugia crops pesticide |
| title | Dynamic Analysis and Optimal Control of the Spread of Tungro Virus Disease in Rice Plants Considering Refugia Planting and Pesticide Application |
| title_full | Dynamic Analysis and Optimal Control of the Spread of Tungro Virus Disease in Rice Plants Considering Refugia Planting and Pesticide Application |
| title_fullStr | Dynamic Analysis and Optimal Control of the Spread of Tungro Virus Disease in Rice Plants Considering Refugia Planting and Pesticide Application |
| title_full_unstemmed | Dynamic Analysis and Optimal Control of the Spread of Tungro Virus Disease in Rice Plants Considering Refugia Planting and Pesticide Application |
| title_short | Dynamic Analysis and Optimal Control of the Spread of Tungro Virus Disease in Rice Plants Considering Refugia Planting and Pesticide Application |
| title_sort | dynamic analysis and optimal control of the spread of tungro virus disease in rice plants considering refugia planting and pesticide application |
| topic | dynamic analysis sensitivity analysis optimal control refugia crops pesticide |
| url | https://www.mdpi.com/2227-7390/12/24/3979 |
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