Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme
Abstract
:1. Introduction
2. Basic Model Structure
- Only healthy cuttings are selected for propagation.
- Diseased cassava plants may be substantially less vigorous than healthy ones, as evidenced by a consistent loss rate due to disease. Any roguing procedures are also considered to increase the loss rate of unhealthy plants.
- The replanting rate for the cassava plant is higher than that for the harvest and roguing rates.
- The propagation rate of whiteflies is higher than the death rate.
- Once a cassava plant gets infected, it remains infectious until recovered or harvested.
- The rate at which the whiteflies vector gets infected from the infected cassava plants and the rate at which the virus acquisition by non-infective vectors is equal.
- Once whiteflies get infected, they remain infectious for life, but their offspring are not infective.
3. Fractional Operators
4. CMD Model with Caputo–Fabrizio Derivative
4.1. Existence and Uniqueness of CMD Model
4.2. Stability Analysis
5. Numerical Results
5.1. Numerical Method
5.2. Numerical Simulations
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description | Value |
---|---|---|
a | The maximum replanting rate | 0.05 day−1 |
k | The maximum abundance of cassava plant | 0.5 m−2 |
The recovery rate of cassava plant | 0.003 day−1 | |
r | Infection rate | 0.008 vector−1 day−1 |
The harvesting rate of cassava plant | 0.003 day−1 | |
g | Roguing/removed plant rate | 0.003 day−1 |
b | The growth rate of whitefly vectors | 0.2 day−1 |
The external sources of infections | 1 vector−1 day−1 | |
The maximum abundance of vectors | 500 plant−1 | |
m | The rate of virus acquisition by non-infective vectors | 0.008 plant−1 day−1 |
Death rate of whitefly vectors | 0.12 day−1 |
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Abdullah, T.Q.S.; Huang, G.; Al-Sadi, W.; Aboelmagd, Y.; Mobarak, W. Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme. Mathematics 2024, 12, 2386. https://doi.org/10.3390/math12152386
Abdullah TQS, Huang G, Al-Sadi W, Aboelmagd Y, Mobarak W. Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme. Mathematics. 2024; 12(15):2386. https://doi.org/10.3390/math12152386
Chicago/Turabian StyleAbdullah, Tariq Q. S., Gang Huang, Wadhah Al-Sadi, Yasser Aboelmagd, and Wael Mobarak. 2024. "Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme" Mathematics 12, no. 15: 2386. https://doi.org/10.3390/math12152386
APA StyleAbdullah, T. Q. S., Huang, G., Al-Sadi, W., Aboelmagd, Y., & Mobarak, W. (2024). Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme. Mathematics, 12(15), 2386. https://doi.org/10.3390/math12152386