Analyzing population dynamics models via Sumudu transform

Volume 29, Issue 3, pp 283--294 https://doi.org/10.22436/jmcs.029.03.07

Publication Date: November 02, 2022 Submission Date: September 18, 2021 Revision Date: October 04, 2021 Accteptance Date: October 07, 2021

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Authors

M. O. Aibinu - Institute for Systems Science \(\&\) KZN e-Skills CoLab, Durban University of Technology, Durban 4000, South Africa. - DSI-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa. - National Institute for Theoretical and Computational Sciences (NITheCS), South Africa. S. C. Thakur - KZN e-Skills CoLab, Durban University of Technology, Durban 4000, South Africa. S. Moyo - Institute for Systems Science \(\&\) Office of the DVC Research, Innovation \(\&\) Engagement, Milena Court, Durban University of Technology, Durban 4000, South Africa.

Abstract

This study demonstrates how to construct the solutions of a more general form of population dynamics models via a blend of variational iterative method with Sumudu transform. Evolution of population growth models are presented and new models which are more general, are proposed in form of delay differential equations of pantograph type. This study presents suitable reformulation and reconstruction for some existing population growth models in terms of delay differential equations of pantograph type. Also, presentation is given on innovative ways to obtain the solutions of population growth models where other analytic methods fail. Stimulating procedures for finding patterns and regularities in seemingly chaotic processes are elucidated in this paper. Some single and interacting species population models are illustrated graphically and analyzed. How, when and why the changes in population sizes occur can be deduced through this study.

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Keywords

• Population size
• models
• Sumudu transform
• pantograph type equations

MSC

•  34A08
•  65M70
•  33C45

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