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Dynamical of curative and preventive treatments in a two-stage plant disease model of fractional order

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  • El-Sayed, A.M.A.
  • Rida, S.Z.
  • Gaber, Y.A.

Abstract

Plants are really important for the planet and for all living things. Plants absorb carbon dioxide and release oxygen from their leaves, which humans and other animals need to breathe. Living things need plants to live - they eat them and live on them. Therefore, understanding plant disease dynamics is important as it can provide insightful knowledge on plant disease transmission. So, in this work, we introduce the fractional order model for the plant diseases in a two-stage infection. We show that this model possesses non-negative solutions as desired in any population dynamics. We discuss the stability of a disease free and an endemic equilibrium for the proposed model. We carry out numerical solutions to demonstrate the theoretical analysis by applying the fractional Euler method (FEM).

Suggested Citation

  • El-Sayed, A.M.A. & Rida, S.Z. & Gaber, Y.A., 2020. "Dynamical of curative and preventive treatments in a two-stage plant disease model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302794
    DOI: 10.1016/j.chaos.2020.109879
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    References listed on IDEAS

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    1. Jajarmi, Amin & Arshad, Sadia & Baleanu, Dumitru, 2019. "A new fractional modelling and control strategy for the outbreak of dengue fever," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2020. "Save the pine forests of wilt disease using a fractional optimal control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Tongqian Zhang & Xinzhu Meng & Yi Song & Zhenqing Li, 2012. "Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, April.
    5. I. Ameen & M. Hidan & Z. Mostefaoui & H.M. Ali, 2020. "Fractional Optimal Control with Fish Consumption to Prevent the Risk of Coronary Heart Disease," Complexity, Hindawi, vol. 2020, pages 1-13, February.
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    1. Shaw, Pawan Kumar & Kumar, Sunil & Momani, Shaher & Hadid, Samir, 2022. "Dynamical analysis of fractional plant disease model with curative and preventive treatments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Rika Amelia & Nursanti Anggriani & Asep K. Supriatna & Noor Istifadah, 2022. "Mathematical Model for Analyzing the Dynamics of Tungro Virus Disease in Rice: A Systematic Literature Review," Mathematics, MDPI, vol. 10(16), pages 1-18, August.

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