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Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

Author

Listed:
  • Arjun Hasibuan

    (Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Asep Kuswandi Supriatna

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Endang Rusyaman

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Md. Haider Ali Biswas

    (Mathematics Discipline, Khulna University, Khulna 9208, Bangladesh)

Abstract

The United Nations has predicted the growth of the human population to reach 8.405 billion by mid-2023, which is a 70% increase in global food demand. This growth will significantly affect global food security, mainly marine resources. Most marine resources exist within complex biological food webs, including predator–prey interactions. These interactions have been researched for decades by mathematicians, who have spent their efforts developing realistic and applicable models. Therefore, this paper systematically reviews articles related to predator–prey models considering the harvesting of resources in marine protected areas. The review identifies future remodeling problems using several mathematical tools. It also proposes the use of feedback linearization consisting of both the approximation and exact methods as an alternative to Jacobian linearization. The results show that in an optimal control analysis, adding a constraint in the form of population density greater than or equal to the positive threshold value should be considered to ensure an ecologically sustainable policy. This research and future developments in this area can significantly contribute to achieving the Sustainable Development Goals (SDGs) set for 2030.

Suggested Citation

  • Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review," Sustainability, MDPI, vol. 15(16), pages 1-23, August.
    • Handle: RePEc:gam:jsusta:v:15:y:2023:i:16:p:12291-:d:1215646
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    References listed on IDEAS

    as
    1. Hai-Feng Huo & Xiaohong Wang & Carlos Castillo-Chavez, 2011. "Dynamics of a Stage-Structured Leslie-Gower Predator-Prey Model," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-22, June.
    2. Mi Wang, 2023. "Diffusion-Induced Instability of the Periodic Solutions in a Reaction-Diffusion Predator-Prey Model with Dormancy of Predators," Mathematics, MDPI, vol. 11(8), pages 1-16, April.
    3. Hai-Feng Huo & Hui-Min Jiang & Xin-You Meng, 2012. "A Dynamic Model for Fishery Resource with Reserve Area and Taxation," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, January.
    4. Bentout, Soufiane & Djilali, Salih & Kumar, Sunil, 2021. "Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    5. Binhao Hong & Chunrui Zhang, 2023. "Neimark–Sacker Bifurcation of a Discrete-Time Predator–Prey Model with Prey Refuge Effect," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    6. Yuanfu Shao & Weili Kong, 2022. "A Predator–Prey Model with Beddington–DeAngelis Functional Response and Multiple Delays in Deterministic and Stochastic Environments," Mathematics, MDPI, vol. 10(18), pages 1-25, September.
    7. Pei, Yongzhen & Chen, Miaomiao & Liang, Xiyin & Li, Changguo, 2019. "Model-based on fishery management systems with selective harvest policies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 377-395.
    8. Ghanbari, Behzad & Djilali, Salih, 2020. "Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    9. Xiongxiong Du & Xiaoling Han & Ceyu Lei, 2022. "Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    10. Gildeberto S. Cardoso & Leizer Schnitman, 2011. "Analysis of Exact Linearization and Aproximate Feedback Linearization Techniques," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-17, May.
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