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Updated: Feb 20, 2026
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Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
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New nonlinear model of population growth
Badr Saad T Alkahtani1, Abdon Atangana2, Ilknur Koca3
1Department of Mathematical, Colle of Science, King Saud University, P.O.Box 1142, Riyadh, 11989, Saudi Arabia.
Plos One
|October 25, 2017
Summary
This study introduces a novel fractional differentiation population growth model incorporating sexuality. The research confirms a unique solution and provides a numerical method for this advanced population dynamics model.
Area of Science:
- Mathematical Biology
- Dynamical Systems
- Fractional Calculus
Background:
- Traditional population growth models often lack the complexity to capture nuanced biological factors.
- Fractional calculus offers a powerful framework for modeling systems with memory and hereditary properties.
Purpose of the Study:
- To revise existing population growth models using fractional differentiation.
- To introduce a new population model incorporating the factor of sexuality.
- To analyze the existence and uniqueness of solutions for the proposed model.
Main Methods:
- Application of fractional differentiation with a generalized Mittag-Leffler function kernel.
- Theoretical analysis for the existence and uniqueness of solutions.
- Development and implementation of a numerical solution method.
Main Results:
- A novel fractional population growth model is successfully formulated.
- The existence and uniqueness of a solution for the model were rigorously investigated.
- A numerical approach was developed and validated for solving the model.
Conclusions:
- The proposed fractional model offers a more sophisticated approach to population dynamics, including sexuality.
- Fractional calculus provides a suitable mathematical tool for enhancing population growth models.
- The study demonstrates the feasibility and analytical tractability of the new model.
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