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Article

Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps

by
Moustafa El-Shahed
1,*,
Asma Al-Nujiban
2 and
Nagdy F. Abdel-Baky
3,4
1
Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, P.O. Box 3771, Unaizah 51911, Saudi Arabia
2
Department of Biology, Unaizah College of Sciences and Arts, Qassim University, P.O. Box 3771, Unaizah 51911, Saudi Arabia
3
Department of Plant Production and Protection, College of Agriculture and Veterinary Medicine, Qassim University, Buraidah 51452, Saudi Arabia
4
Economic Entomology Deptartment, Faculty of Agriculture, Mansoura University, Mansoura 35516, Egypt
*
Author to whom correspondence should be addressed.
Axioms 2022, 11(7), 334; https://doi.org/10.3390/axioms11070334
Submission received: 3 June 2022 / Revised: 30 June 2022 / Accepted: 7 July 2022 / Published: 10 July 2022
(This article belongs to the Special Issue Stochastic Modelling and Statistical Methods in Earth and Environmental Sciences)
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Abstract

This paper deals with the mathematical modelling of the red palm weevil (RPW), Rhynchophorus ferrugineus (Olivier) (Coleoptera: Curculionidae), in date palms using chemical control by utilizing injection and sex pheromone traps. A deterministic and stochastic model for RPW is proposed and analyzed. The existence of a positive global solution for the stochastic RPW model is investigated, and the conditions for the extinction of RPWs from the stochastic system are obtained. The adequate criteria for the presence of a unique ergodic stationary distribution for the RPW system are established by creating suitable Lyapunov functions. The impact of chemical injection and pheromone traps on RPW is demonstrated. The importance of environmental noise on RPW is highlighted and simulated using the Milstein method.
Keywords: stochastic models; stability; sex pheromone trap; Rhynchophorus ferrugineus; chemical injection stochastic models; stability; sex pheromone trap; Rhynchophorus ferrugineus; chemical injection

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MDPI and ACS Style

El-Shahed, M.; Al-Nujiban, A.; Abdel-Baky, N.F. Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps. Axioms 2022, 11, 334. https://doi.org/10.3390/axioms11070334

AMA Style

El-Shahed M, Al-Nujiban A, Abdel-Baky NF. Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps. Axioms. 2022; 11(7):334. https://doi.org/10.3390/axioms11070334

Chicago/Turabian Style

El-Shahed, Moustafa, Asma Al-Nujiban, and Nagdy F. Abdel-Baky. 2022. "Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps" Axioms 11, no. 7: 334. https://doi.org/10.3390/axioms11070334

APA Style

El-Shahed, M., Al-Nujiban, A., & Abdel-Baky, N. F. (2022). Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps. Axioms, 11(7), 334. https://doi.org/10.3390/axioms11070334

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