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Full Delay Logistic Population Model with Sustainable Harvesting

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Listed:
  • Martin Anokye
  • Elvis Kobina Donkoh
  • Michael Fosu Ofori
  • Agnes Adom-Konadu

Abstract

The paper studies the dynamics of a full delay‐logistic population model incorporated with a proportionate harvesting function. The study discusses the stability of the model in comparison with the well‐known Hutchinson logistic growth equation with harvesting function using the rate of harvesting as a bifurcation parameter to determine sustainable harvesting rate even at a bigger time delay of τ = 3.00. In all cases, the Hutchinson equation with harvesting was forced to converge to equilibrium using an additional and a different time delay parameter, a deficiency previous researchers have failed to address when the Hutchinson model is used for this purpose. The population fluctuations are catered for with this model making the estimated maximum sustainable growth and harvest reflect realities as this model drastically reduces time‐delay associated oscillations compared to the well‐known Hutchinson delayed logistic models. The numerical simulations were be done using the MatLab Software.

Suggested Citation

  • Martin Anokye & Elvis Kobina Donkoh & Michael Fosu Ofori & Agnes Adom-Konadu, 2022. "Full Delay Logistic Population Model with Sustainable Harvesting," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnljam:v:2022:y:2022:i:1:n:6777827
    DOI: 10.1155/2022/6777827
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    References listed on IDEAS

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    1. repec:hin:complx:9876013 is not listed on IDEAS
    2. Monika Joanna Piotrowska & Marek Bodnar, 2014. "Logistic Equation with Treatment Function and Discrete Delays," Mathematical Population Studies, Taylor & Francis Journals, vol. 21(3), pages 166-183, September.
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    Cited by:

    1. Tomasz Popławski, 2025. "Long-Term Forecast of Peak Power Demand for Poland—Construction and Use of Simplified Forecasting Models," Energies, MDPI, vol. 18(13), pages 1-17, July.
    2. Rashi, & Singh, Suruchi & Umrao, Anuj Kumar & Singh, Harendra Pal & Srivastava, Prashant K., 2025. "Cooperation and harvesting-induced delays in a predator–prey model with prey fear response: A crossing curves approach," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    3. Martin Anokye & Sampson Z. Nkangbi & Agnes A. Konadu & Albert L. Sackitey & John A. Mensah & Luca Guerrini & Massimiliano Ferrara, 2025. "Stability analysis of a delay logistic growth model with nonlinear harvesting," Quality & Quantity: International Journal of Methodology, Springer, vol. 59(6), pages 5253-5268, December.

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    1. Martin Anokye & Sampson Z. Nkangbi & Agnes A. Konadu & Albert L. Sackitey & John A. Mensah & Luca Guerrini & Massimiliano Ferrara, 2025. "Stability analysis of a delay logistic growth model with nonlinear harvesting," Quality & Quantity: International Journal of Methodology, Springer, vol. 59(6), pages 5253-5268, December.

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