Open Access

ARTICLE

Deterministic and Stochastic Fractional Order Model for Lesser Date Moth

by Moustafa El-shahed^1,*, Asmaa M. Al-Dububan²

1 Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, P.O. Box 3771, Unaizah, 51911, Saudi Arabia
2 Department of Mathematics, Buraydah College of Sciences and Arts, Qassim University, P.O. Box 1162, Buraydah, 51431, Saudi Arabia

* Corresponding Author: Moustafa El-shahed. Email:

Computer Systems Science and Engineering 2022, 40(2), 749-764. https://doi.org/10.32604/csse.2022.019655

Received 21 April 2021; Accepted 23 May 2021; Issue published 09 September 2021

Abstract

In this paper, a deterministic and stochastic fractional order model for lesser date moth (LDM) using mating disruption and natural enemies is proposed and analysed. The interaction between LDM larvae, fertilized LDM female, unfertilized LDM female, LDM male and the natural enemy is investigated. In order to clarify the characteristics of the proposed deterministic fractional order model, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions of the proposed fractional-order model are examined. In addition, some sufficient conditions are obtained to ensure the local and global stability of equilibrium points. The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem. Numerical simulations are conducted to illustrate the properties of the proposed fractional order model with respect to the intrinsic growth rate of the LDM larvae, natural enemy’s mortality rate, predation rate, sex pheromone trap parameter, fractional order and environmental noise. The impact of mating disruption on lesser date moth is demonstrated. Also, a numerical approximation method is developed for the proposed stochastic fractional-order model.

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