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A delayed plant disease model with Caputo fractional derivatives
Pushpendra Kumar1, Dumitru Baleanu2,3, Vedat Suat Erturk4
1Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609 India.
Advances in Continuous and Discrete Models
|April 22, 2022
Summary
This study introduces a fractional mathematical model to understand vector-borne plant epidemics, incorporating memory effects and time delays. Novel results reveal how fractional calculus and infection rates impact disease dynamics.
Area of Science:
- Epidemiology
- Mathematical Biology
- Fractional Calculus
Background:
- Vector-borne plant diseases pose significant threats to agriculture.
- Mathematical models are crucial for understanding disease dynamics.
- Fractional calculus offers advanced tools for modeling systems with memory effects.
Purpose of the Study:
- To analyze a time-delay Caputo-type fractional mathematical model for vector-borne plant epidemics.
- To investigate the impact of the Beddington-DeAngelis functional response on disease structure.
- To explore the role of memory effects and time delays in plant disease dynamics.
Main Methods:
- Utilizing fixed-point theorems to prove the existence and uniqueness of global solutions.
- Employing the Adams-Bashforth-Moulton predictor-corrector algorithm for numerical simulations.
- Applying fractional derivatives, specifically the Caputo derivative, to incorporate memory.
Main Results:
- Demonstrated the existence of a unique global solution for the fractional model.
- Graphical interpretations revealed variations in disease dynamics with changing fractional orders and time delays.
- Investigated the influence of infection rates on susceptible and infectious plant populations.
Conclusions:
- Fractional derivatives, particularly the Caputo derivative, are effective in modeling plant epidemiology with memory.
- Time delays and infection rates significantly influence the dynamics of vector-borne plant diseases.
- The study highlights the utility of fractional calculus in understanding complex epidemiological systems.
Keywords:
Caputo fractional derivativeCrowding effectDisease resistanceFractional mathematical modelIncubation periodPredictor–corrector algorithmTime-delayMore Related Videos
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