Fractal-Fractional Caputo Maize Streak Virus Disease Model
Maize is one of the most extensively produced cereals in the world. The maize streak virus primarily infects maize but can also infect over 80 other grass species. Leafhoppers are the primary vectors of the maize streak virus. When feeding on plants, susceptible vectors can acquire the virus from in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/2/189 |
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| author | Joseph Ackora-Prah Baba Seidu Eric Okyere Joshua K. K. Asamoah |
| author_facet | Joseph Ackora-Prah Baba Seidu Eric Okyere Joshua K. K. Asamoah |
| author_sort | Joseph Ackora-Prah |
| collection | DOAJ |
| description | Maize is one of the most extensively produced cereals in the world. The maize streak virus primarily infects maize but can also infect over 80 other grass species. Leafhoppers are the primary vectors of the maize streak virus. When feeding on plants, susceptible vectors can acquire the virus from infected plants, and infected vectors can transmit the virus to susceptible plants. However, because maize is normally patchy and leafhoppers are mobile, leafhoppers will always be foraging for food. Therefore, we want to look at how leafhoppers interact on maize farms using Holling’s Type III functional response in a Caputo fractal-fractional derivative sense. We show that the proposed model has unique positive solutions within a feasible region. We employed the Newton polynomial scheme to numerically simulate the proposed model to illustrate the qualitative results obtained. We also studied the relationship between the state variables and some epidemiological factors captured as model parameters. We observed that the integer-order versions of the model exaggerate the impact of the disease. We also observe that the increase in the leafhopper infestation on maize fields has a devastating effect on the health of maize plants and the subsequent yield. Furthermore, we noticed that varying the conversion rate of the infected leafhopper leads to a crossover effect in the number of healthy maize after 82 days. We also show the dynamics of varying the maize streak virus transmission rates. It indicates that when preventive measures are taken to reduce the transmission rates, it will reduce the low-yielding effect of maize due to the maize streak virus disease. |
| first_indexed | 2024-03-11T08:48:15Z |
| format | Article |
| id | doaj.art-c2d287f9cbd0436aac1650a203206828 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T08:48:15Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-c2d287f9cbd0436aac1650a2032068282023-11-16T20:37:13ZengMDPI AGFractal and Fractional2504-31102023-02-017218910.3390/fractalfract7020189Fractal-Fractional Caputo Maize Streak Virus Disease ModelJoseph Ackora-Prah0Baba Seidu1Eric Okyere2Joshua K. K. Asamoah3Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, GhanaDepartment of Mathematics, Faculty of Mathematical Sciences, C. K. Tedam University of Technology and Applied Sciences, Navrongo UK-0215-5321, GhanaDepartment of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, GhanaDepartment of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, GhanaMaize is one of the most extensively produced cereals in the world. The maize streak virus primarily infects maize but can also infect over 80 other grass species. Leafhoppers are the primary vectors of the maize streak virus. When feeding on plants, susceptible vectors can acquire the virus from infected plants, and infected vectors can transmit the virus to susceptible plants. However, because maize is normally patchy and leafhoppers are mobile, leafhoppers will always be foraging for food. Therefore, we want to look at how leafhoppers interact on maize farms using Holling’s Type III functional response in a Caputo fractal-fractional derivative sense. We show that the proposed model has unique positive solutions within a feasible region. We employed the Newton polynomial scheme to numerically simulate the proposed model to illustrate the qualitative results obtained. We also studied the relationship between the state variables and some epidemiological factors captured as model parameters. We observed that the integer-order versions of the model exaggerate the impact of the disease. We also observe that the increase in the leafhopper infestation on maize fields has a devastating effect on the health of maize plants and the subsequent yield. Furthermore, we noticed that varying the conversion rate of the infected leafhopper leads to a crossover effect in the number of healthy maize after 82 days. We also show the dynamics of varying the maize streak virus transmission rates. It indicates that when preventive measures are taken to reduce the transmission rates, it will reduce the low-yielding effect of maize due to the maize streak virus disease.https://www.mdpi.com/2504-3110/7/2/189Caputo derivativefractal-fractionalmaize diseaseHolling’s Type IIIfunctional response |
| spellingShingle | Joseph Ackora-Prah Baba Seidu Eric Okyere Joshua K. K. Asamoah Fractal-Fractional Caputo Maize Streak Virus Disease Model Fractal and Fractional Caputo derivative fractal-fractional maize disease Holling’s Type III functional response |
| title | Fractal-Fractional Caputo Maize Streak Virus Disease Model |
| title_full | Fractal-Fractional Caputo Maize Streak Virus Disease Model |
| title_fullStr | Fractal-Fractional Caputo Maize Streak Virus Disease Model |
| title_full_unstemmed | Fractal-Fractional Caputo Maize Streak Virus Disease Model |
| title_short | Fractal-Fractional Caputo Maize Streak Virus Disease Model |
| title_sort | fractal fractional caputo maize streak virus disease model |
| topic | Caputo derivative fractal-fractional maize disease Holling’s Type III functional response |
| url | https://www.mdpi.com/2504-3110/7/2/189 |
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