Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The work represents a novelty study of dynamical systems applied to water pollutants, by the title of the paper one is lead to think about it as a purely numerical analysis, but I was gladly surprised to find analytical results and proves of lemmas and theorems to sustain the simulations of the authors. This in itself is valuable, since stability and asymptotic behavior can be studied in the context of mathematical analysis, not jus as plausibility argumentations via a series of numerical experiments. Their findings suggest multiple applications in polluted water remediation as a species competition, thus implying low costs in time and resources. Although the authors do not mention the numerical scheme which they use to solve their model differential equations, this is not of concern since nowadays typically one just makes use of specific libraries and functions already available. In sum, this work is highly relevant, thus my recommendation of publishing it as it is.

Author Response

Thank you for the opportunity to revise our manuscript. We appreciate the careful review and constructive suggestions and comments.

Reviewer 2 Report

Comments and Suggestions for Authors

Review of the article by Nada A. Almuallem and Miled El Hajji
Global Dynamics of a Multi-Population Water Pollutant Model with Distributed Delays

        In the article, the authors present a mathematical model describing the dynamics of dispersed water pollutants and their interaction with two different host populations. This model is based on a system of integro-differential equations that incorporate several distributed delays to realistically account for time delays in the infection process. The authors justify the correctness of the model by proving the non-negativity and ultimate boundedness of the solutions, which confirms the existence of a positively invariant feasible region. The mathematical model presented in the work can be used to manage dispersed water pollution processes, considering the contribution of various sources, time delays, and targeted measures to ensure ecological sustainability.

         Conclusion. The research direction is relevant, and the obtained results possess scientific novelty. The work can be recommended for publication in the scientific journal Mathematics.

Author Response

Thank you for the opportunity to revise our manuscript. We appreciate the careful review and constructive suggestions and comments.

Reviewer 3 Report

Comments and Suggestions for Authors

see the report

Comments for author File: Comments.pdf

Author Response

Thank you for the opportunity to revise our manuscript. We appreciate the careful review and constructive suggestions and comments. We have revised the manuscript accordingly and provided specific answers in the attached PDF file.

Author Response File: Author Response.pdf