Isaac Scientific Publishing

Advances in Analysis

A Fractional-Order Model for the Spread of Pests in Tea Plants

Download PDF (1088.5 KB) PP. 68 - 79 Pub. Date: October 25, 2016

DOI: 10.22606/aan.2016.12002


  • Moustafa El-Shahed*
    Department of Mathematics, Faculty of Arts and Sciences, Qassim University, P.O. Box 3771, Qassim, Unizah 51911, Saudi Arabia.
  • A. M. Ahmed

    Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, P.O. Box: 11884, Cairo, Egypt
  • Ibrahim. M. E. Abdelstar

    Quantitative Methods Unit, Faculty of Business and Economics, Qassim University, P.O. Box 6633, Qassim, Buraidah 51452, Saudi Arabia


In this paper, a fractional-order model for the spread of pests in tea plants is presented. This model consists of three components: tea plant, pest, and predator. The stability of the boundary and positive fixed points is studied. The global stability properties of the positive equilibrium point are also investigated. In addition, fractional Hopf bifurcation conditions for the model are proposed. The generalized Adams-Bashforth-Moulton method is used to solve and simulate the system of fractional differential equations.


Natural enemy; fractional order; stability; numerical method.


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