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Dynamical analysis of fractional plant disease model with curative and preventive treatments

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  • Shaw, Pawan Kumar
  • Kumar, Sunil
  • Momani, Shaher
  • Hadid, Samir

Abstract

Food security has become a major concern as the human population grows. Agriculture is crucial in this environment. The majority of staple meals are derived from plants. Plant diseases, on the other hand, can lower food production and quality. In this paper, two stage plant disease (TSPD) dynamics can be studied using a fractional order model. Here we used two fractional operator: Caputo fractional derivative (CFD) and Caputo–Fabrizio fractional derivative (CFFD) each of arbitrary order ϖ∈(0,1]. We evaluate the effects of curative and preventive treatments on plant disease transmission dynamics in the concerned model. We demonstrate that this model has non-negative solutions, which is desirable in population dynamics. For the suggested model, we discuss the stability of a disease-free and endemic equilibrium. For numerical simulation, we used generalized fractional RK2 scheme, Adams–Bashforth Moulton (ABM) scheme, and three step fractional Adam–Bashforth scheme (ABS) to visualize the outcomes of the concerned model. We discovered that combining curative and preventive treatment can help to reduce the number of diseased plants.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008840
    DOI: 10.1016/j.chaos.2022.112705
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    References listed on IDEAS

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    1. 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).
    2. Agarwal, Praveen & Singh, Ram, 2020. "Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    3. Muhammad Sarmad Arshad & Dumitru Baleanu & Muhammad Bilal Riaz & Muhammad Abbas & Qasem M. Al-Mdallal, 2020. "A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-8, June.
    4. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2019. "A fractional mathematical model of breast cancer competition model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 38-54.
    5. 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).
    6. 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. Stefania Tomasiello & Jorge E. Macías-Díaz, 2023. "A Mini-Review on Recent Fractional Models for Agri-Food Problems," Mathematics, MDPI, vol. 11(10), pages 1-12, May.

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