Optimal Control Techniques in Managing Red Palm Weevil Infestations: A Mathematical Approach

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DOI: https://doi.org/10.28924/2291-8639-22-2024-148
Published: Sep 2, 2024
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Lamya Al-Maghamsi, Ymnah Alruwaily, Moustafa El-Shahed, Optimal Control Techniques in Managing Red Palm Weevil Infestations: A Mathematical Approach, Int. J. Anal. Appl., 22 (2024), 148.

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Lamya Al-Maghamsi, Ymnah Alruwaily, Moustafa El-Shahed

Abstract

This article introduces a mathematical analysis of the red palm weevil (RPW) model that incorporates optimal control techniques. The investigation delves into the dynamics among date palm trees, the RPW, and tree micro-injection. The analysis assesses the impact of sex pheromone traps and tree trunk injections on the RPW population. Sufficient constraints are identified to provide both local stability and global stability analysis of equilibrium points. The paper uses Sotomayor’s theorem as a guide to compute local bifurcations near equilibrium points. The study concludes that adopting control strategies shows to a substantial decline in the RPW population, ultimately resulting in extinction. Numerical simulations are employed to visually illustrate and support the theoretical findings.

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References

  1. L.I. El-Juhany, Degradation of Date Palm Trees and Date Production in Arab Countries: Causes and Potential Rehabilitation, Aust. J. Basic Appl. Sci. 4 (2010), 3998–4010.
  2. J.M. Al-Khayri, Date Palm Phoenix dactylifera L. Micropropagation, in: S.M. Jain, H. Häggman (Eds.), Protocols for Micropropagation of Woody Trees and Fruits, Springer, Dordrecht, 2007: pp. 509–526. https://doi.org/10.1007/978-1-4020-6352-7_46.
  3. A. Levi-Zada, D. Fefer, L. Anshelevitch, A. Litovsky, M. Bengtsson, G. Gindin, V. Soroker, Identification of the Sex Pheromone of the Lesser Date Moth, Batrachedra Amydraula, Using Sequential SPME Auto-Sampling, Tetrahedron Lett. 52 (2011), 4550–4553. https://doi.org/10.1016/j.tetlet.2011.06.091.
  4. M. A. Al-Deeb, H. A. Al-Dhaheri, Use of a Pheromone-Baited Trap to Monitor the Population of the Lesser Date Moth Batrachedra Amydraula (Lepidoptera: Batrachedridae) in the UAE, J. Entomol. Zool. Stud. 5 (2017), 2572–2575.
  5. M.S. Hoddle, A.H. Al-Abbad, H.A.F. El-Shafie, J.R. Faleiro, A.A. Sallam, C.D. Hoddle, Assessing the Impact of Areawide Pheromone Trapping, Pesticide Applications, and Eradication of Infested Date Palms for Rhynchophorus Ferrugineus (Coleoptera: Curculionidae) Management in Al Ghowaybah, Saudi Arabia, Crop Protect. 53 (2013), 152–160. https://doi.org/10.1016/j.cropro.2013.07.010.
  6. I. Milosavljevi´c, H.A.F. El-Shafie, J.R. Faleiro, C.D. Hoddle, M. Lewis, M.S. Hoddle, Palmageddon: The Wasting of Ornamental Palms by Invasive Palm Weevils, Rhynchophorus spp., J. Pest. Sci. 92 (2018), 143–156. https://doi.org/10.1007/s10340-018-1044-3.
  7. M. Ponce-Méndez, M.A. García-Martínez, R. Serna-Lagunes, R. Lasa-Covarrubias, E. Presa-Parra, J. MurguíaGonzález, C. Llarena-Hernández, Local Agricultural Management Filters Morphological Traits of the South American Palm Weevil (Rhynchophorus palmarum L.; Coleoptera: Curculionidae) in Ornamental Palm Plantations, Agronomy. 12 (2022), 2371. https://doi.org/10.3390/agronomy12102371.
  8. R.T. Carde, Using Pheromones to Disrupt Mating of Moth Pests, In: Perspectives in Ecological Theory and Integrated Pest Management, Cambridge University Press, Cambridge, pp. 122–169, 2007.
  9. W. Wakil, J. Romeno Faleiro, T.A. Miller, eds., Sustainable Pest Management in Date Palm: Current Status and Emerging Challenges, Springer, Cham, 2015. https://doi.org/10.1007/978-3-319-24397-9.
  10. P. Witzgall, P. Kirsch, A. Cork, Sex Pheromones and Their Impact on Pest Management, J. Chem. Ecol. 36 (2010), 80–100. https://doi.org/10.1007/s10886-009-9737-y.
  11. H.J. Barclay, G.J.R. Judd, Models for Mating Disruption by Means of Pheromone for Insect Pest Control, Popul. Ecol. 37 (1995), 239–247. https://doi.org/10.1007/bf02515826.
  12. A.I.K. Butt, M. Imran, S. Batool, M.A. Nuwairan, Theoretical Analysis of a COVID-19 CF-Fractional Model to Optimally Control the Spread of Pandemic, Symmetry. 15 (2023), 380. https://doi.org/10.3390/sym15020380.
  13. M. El-Shahed, A.M. Al-Dubiban, Mathematical Modelling of Lesser Date Moth Using Sex Pheromone Traps and Natural Enemies, Math. Probl. Eng. 2021 (2021), 8835321. https://doi.org/10.1155/2021/8835321.
  14. M. El-Shahed, A. Al-Nujiban, N.F. Abdel-Baky, Stochastic Modelling of Red Palm Weevil Using Chemical Injection and Pheromone Traps, Axioms. 11 (2022), 334. https://doi.org/10.3390/axioms11070334.
  15. Y. Alnafisah, M. El-Shahed, Optimal Control of Red Palm Weevil Model Incorporating Sterile Insect Technique, Mechanical Injection, and Pheromone Traps, Alexandria Eng. J. 93 (2024), 382–391. https://doi.org/10.1016/j.aej.2024.02.059.
  16. H. Barclay, P. van den Driessche, Pheromone Trapping Models for Insect Pest Control, Popul. Ecol. 25 (1983), 105–115. https://doi.org/10.1007/bf02528786.
  17. H.J. Barclay, J. Hendrichs, Models for Assessing the Male Annihilation ofBactroceraspp. with Methyl Eugenol Baits, Ann. Entomol. Soc. Amer. 107 (2014), 81–96. https://doi.org/10.1603/an13046.
  18. R. Anguelov, C. Dufourd, Y. Dumont, Mathematical Model for Pest–insect Control Using Mating Disruption and Trapping, Appl. Math. Model. 52 (2017), 437–457. https://doi.org/10.1016/j.apm.2017.07.060.
  19. J.P. Ntahomvukiye, A. Temgoua, S. Bowong, Study of the Population Dynamics of Busseola fusca, Maize Pest, Acta Biotheor. 66 (2018), 379–397. https://doi.org/10.1007/s10441-018-9335-x.
  20. S. Xiang, Y. Pei, X. Liang, Analysis and Optimization Based on a Sex Pheromone and Pesticide Pest Model With Gestation Delay, Int. J. Biomath. 12 (2019), 1950054. https://doi.org/10.1142/s1793524519500542.
  21. M.D. Tapi, L. Bagny-Beilhe, Y. Dumont, Miridae Control Using Sex-Pheromone Traps. Modeling, Analysis and Simulations, Nonlinear Anal.: Real World Appl. 54 (2020), 103082. https://doi.org/10.1016/j.nonrwa.2019.103082.
  22. M. El-shahed, A. M. Al-Dububan, Deterministic and Stochastic Fractional Order Model for Lesser Date Moth, Computer Syst. Sci. Eng. 40 (2022), 749–764. https://doi.org/10.32604/csse.2022.019655.
  23. G. Birkhoff, G. Rota, Ordinary Differential Equation, 4th Edition, Wily, New York, (1989).
  24. K. Hassan, A. Mustafa, M. Hama, An Eco-Epidemiological Model Incorporating Harvesting Factors, Symmetry. 13 (2021), 2179. https://doi.org/10.3390/sym13112179.
  25. W. Feng, N. Rocco, M. Freeze, X. Lu, Mathematical Analysis on an Extended Rosenzweig-Macarthur Model of TriTrophic Food Chain, Discrete Contin. Dyn. Syst. - S. 7 (2014). 1215–1230. https://doi.org/10.3934/dcdss.2014.7.1215.
  26. W. Feng, M. T. Cowen, X. Lu, Coexistence and Asymptotic Stability in Stage-Structured Predator-Prey Models, Math. Biosci. Eng. 11 (2014), 823–839. https://doi.org/10.3934/mbe.2014.11.823.
  27. P. van den Driessche, J. Watmough, Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission, Math. Biosci. 180 (2002), 29–48. https://doi.org/10.1016/s0025-5564(02)00108-6.
  28. A.J. Alqarni, A.S. Rambely, I. Hashim, Dynamic Modelling of Interactions Between Microglia and Endogenous Neural Stem Cells in the Brain During a Stroke, Mathematics. 8 (2020), 132. https://doi.org/10.3390/math8010132.
  29. K. Manna, V. Volpert, M. Banerjee, Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal IntraSpecific Competition for Both the Prey Species, Mathematics. 8 (2020), 101. https://doi.org/10.3390/math8010101.
  30. A.E. Matouk, A.A. Elsadany, E. Ahmed, H.N. Agiza, Dynamical Behavior of Fractional-Order Hastings–powell Food Chain Model and Its Discretization, Commun. Nonlinear Sci. Numer. Simul. 27 (2015), 153–167. https://doi.org/10.1016/j.cnsns.2015.03.004.
  31. L. Perko, Differential Equations and Dynamical Systems, Vol. 7, Texts in Applied Mathematics, Springer, 2013.
  32. L.S. Pontryagin, Mathematical Theory of Optimal Processes, CRC Press, 1987.
  33. J. Chowdhury, F. Al Basir, Y. Takeuchi, M. Ghosh, P.K. Roy, A Mathematical Model for Pest Management in Jatropha Curcas With Integrated Pesticides - An Optimal Control Approach, Ecol. Complex. 37 (2019), 24–31. https://doi.org/10.1016/j.ecocom.2018.12.004.
  34. E. Venturino, P.K. Roy, F. Al Basir, A. Datta, A Model for the Control of the Mosaic Virus Disease in Jatropha Curcas Plantations, Energ. Ecol. Environ. 1 (2016), 360–369. https://doi.org/10.1007/s40974-016-0033-8.
  35. H.T. Alemneh, A.S. Kassa, A.A. Godana, An Optimal Control Model With Cost Effectiveness Analysis of Maize Streak Virus Disease in Maize Plant, Infect. Dis. Model. 6 (2021), 169–182. https://doi.org/10.1016/j.idm.2020.12.001.
  36. N.H. Shah, P.M. Pandya, A.H. Suthar, Optimal Control to Curtail the Spread of COVID-19 Through Social Gatherings: A Mathematical Model, in: Mathematical and Computational Modelling of Covid-19 Transmission, River Publishers, pp. 109–124, 2023.