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A study on the maize streak virus epidemic model by using optimized linearization-based predictor-corrector method in Caputo sense

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  • Kumar, Pushpendra
  • Erturk, Vedat Suat
  • Vellappandi, M.
  • Trinh, Hieu
  • Govindaraj, V.

Abstract

In this article, we study the dynamics of a Maize streak virus (MSV) epidemic model by using the Caputo fractional derivative. Firstly, we define the dynamics of the given fractional-order model by checking the non-negativity and boundedness of the solution, stability of disease-free equilibrium, the existence of a unique solution, and its stability. Then we derive the numerical solution of the proposed model by using an optimized Predictor-Corrector method, which has not yet been applied to solve any kind of epidemic system until now. Our optimized method uses a linear approximation of the proposed nonlinear model to ameliorate the competence of the Predictor-Corrector schemes. To verify the correctness of our results, we plot various graphs by taking different parameter cases at various fractional-order values. Also, Caputo outputs are compared with Atangana-Baleanu-Caputo derivative outputs. Our research shows the usefulness of the proposed optimized Predictor-Corrector method in epidemic studies and for simulating the memory effects in the given MSV system. The solution methodology of the proposed system is the main novelty of this research along with other supporting analyses.

Suggested Citation

  • Kumar, Pushpendra & Erturk, Vedat Suat & Vellappandi, M. & Trinh, Hieu & Govindaraj, V., 2022. "A study on the maize streak virus epidemic model by using optimized linearization-based predictor-corrector method in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002776
    DOI: 10.1016/j.chaos.2022.112067
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    References listed on IDEAS

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    1. Christopher Nicholas Angstmann & Byron Alexander Jacobs & Bruce Ian Henry & Zhuang Xu, 2020. "Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
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    8. Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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    10. Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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