Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model
The continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop prot...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2024-07-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://journals.vu.lt./nonlinear-analysis/article/view/35448 |
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| author | Navnit Jha Akash Yadav Ritesh Pandey A.K. Misra |
| author_facet | Navnit Jha Akash Yadav Ritesh Pandey A.K. Misra |
| author_sort | Navnit Jha |
| collection | DOAJ |
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The continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop protectors, the extensive use of these chemicals adversely affects both human health and the environment. In this research work, we formulate a nonlinear mathematical model using the Caputo fractional (CF) operator to investigate the effects of pesticides on crop yield dynamics. We assume that pesticides are sprayed proportional to the density of pest density and pests not entirely reliant on crops. The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. Furthermore, we have identified the optimal time profile for pesticide spraying rate. This profile proves effective in minimizing both the pest population and the associated costs. To provide a practical illustration of our analytical findings and to showcase the impact of key parameters on the system’s dynamics, we conducted numerical simulations. These simulations are conducted employing the generalized Adams–Bashforth–Moulton method, which allowed us to vividly demonstrate the real-world implications of our research.
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| format | Article |
| id | doaj-art-aa1ae9a46d0241c8a648b3f437003db8 |
| institution | Kabale University |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-aa1ae9a46d0241c8a648b3f437003db82025-02-03T07:06:25ZengVilnius University PressNonlinear Analysis1392-51132335-89632024-07-0129510.15388/namc.2024.29.35448Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional modelNavnit Jha0https://orcid.org/0000-0001-7884-8640Akash Yadav1https://orcid.org/0000-0002-6180-5553Ritesh Pandey2https://orcid.org/0000-0002-9128-3848A.K. Misra3https://orcid.org/0000-0002-2885-9955South Asian UniversityBanaras Hindu UniversityShambhunath Institute of Engineering and TechnologyBanaras Hindu University The continuous growth of the human population raises concerns about food, fiber, and agricultural insecurity. Meeting the escalating demand for agricultural products due to this population surge makes protecting crops from pests becomes imperative. While farmers use chemical pesticides as crop protectors, the extensive use of these chemicals adversely affects both human health and the environment. In this research work, we formulate a nonlinear mathematical model using the Caputo fractional (CF) operator to investigate the effects of pesticides on crop yield dynamics. We assume that pesticides are sprayed proportional to the density of pest density and pests not entirely reliant on crops. The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. Furthermore, we have identified the optimal time profile for pesticide spraying rate. This profile proves effective in minimizing both the pest population and the associated costs. To provide a practical illustration of our analytical findings and to showcase the impact of key parameters on the system’s dynamics, we conducted numerical simulations. These simulations are conducted employing the generalized Adams–Bashforth–Moulton method, which allowed us to vividly demonstrate the real-world implications of our research. https://journals.vu.lt./nonlinear-analysis/article/view/35448mathematical modelcrop productionCaputo fractional derivativepesticidesstability |
| spellingShingle | Navnit Jha Akash Yadav Ritesh Pandey A.K. Misra Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model Nonlinear Analysis mathematical model crop production Caputo fractional derivative pesticides stability |
| title | Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model |
| title_full | Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model |
| title_fullStr | Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model |
| title_full_unstemmed | Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model |
| title_short | Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model |
| title_sort | analyzing crop production unraveling the impact of pests and pesticides through a fractional model |
| topic | mathematical model crop production Caputo fractional derivative pesticides stability |
| url | https://journals.vu.lt./nonlinear-analysis/article/view/35448 |
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