On Integrable Models for the Spread of Disease

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors The author presents the analytical solution of specific models for disease spread that may be useful for identifying disease behavior. The results are interesting. Before considering the document for publication, the author should include in the introduction the state of the art regarding the implications of finding analytical solutions in these types of systems, as well as the limitations that the presented models present in reflecting reality. The descriptions of the figures should include the equations with which they are obtained. In addition, the conclusions section should be included, emphasizing the results and the advantages they provide over numerical solutions to the models.

Author Response

See the attached file

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this work, the author presented some historical models for infectious disease modeling and analyzed them. Below are my comments

1. The citations in this work are not arranged in ascending or descending order.
2. This work lacks discussion and conclusion.
3. What can we learn from this work?
4. What the author presented is similar to the following article. The author must justify what makes their work different. https://www.mdpi.com/2079-7737/11/12/1825

Author Response

See the attachment

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Author,

Thank you for the opportunity to review your manuscript. The subject you address is certainly interesting, and the technical details presented are valuable. In particular, the attempt to connect integrable versions of epidemic models with a documented COVID-19 case is a promising direction.

However, the manuscript in its current form appears incomplete and requires substantial improvements before it could be considered for publication. My main concerns are as follows: 

 

• Introduction – The introduction needs to be expanded and improved to provide clearer context, motivation, and relation to existing literature.

• Conclusions – A dedicated Conclusions section is essential and currently missing.

• Figures – The figures require improvement, for example by adding proper legends and clarifying the information presented.

• Equations – There are typographical issues that must be corrected. For instance, between lines 60 and 61 the equation should use the correct subscript notation JSJ_SJS​.

• Overall presentation – While the manuscript contains many technical details, it lacks the style, focus, and scope expected for this journal.

In summary, your work seems to be the beginning of an interesting research project, but at this stage it does not yet reach the level of a complete and publishable article

Author Response

see the attachment

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The paper "On Integrable Models for the Spread of Disease", by G. Hovhannisyan, concerns the development of an integrable version of an SIR-like model with applications to the COVID-19 pandemic.

Even though in principle this paper might be of interest, it completely lacks a solid structure. In my opinion, it could only be reconsidered for publication after major revisions.

1. The novelty and significance of this study are not clearly established. Why should this approach be of interest? What potential impact could it have on applications? Accordingly, what are the possible perspectives for future research? In its current form, it looks like a mathematical (technical) exercise. 

2. There is a complete lack of engagement with the recent literature on the topic. In particular, the author neglects the kinetic-theory approach to epidemic modeling. For instance, the following references could be considered:

   • Dimarco, G., Perthame, B., Toscani, G., & Zanella, M. (2021). Kinetic models for epidemic dynamics with social heterogeneity. Journal of Mathematical Biology, 83(1), 4.

   • Della Marca, R., Loy, N., & Tosin, A. (2023). An SIR model with viral load-dependent transmission. Journal of Mathematical Biology, 86(4), 61.

   • Della Marca, R., Loy, N., & Menale, M. (2023). Intransigent vs. volatile opinions in a kinetic epidemic model with imitation game dynamics. Mathematical Medicine and Biology: A Journal of the IMA, 40(2), 111–140.

3. The numerous computations presented throughout the paper should be better motivated and explained to improve readability. In particular, the extact solutions are not clear in their derivation and motivation.

4. The numerical methods employed for the simulations are not specified. Which methods have been used? How does the integrable structure, developed along the paper, affect the efficiency or reliability of these methods?

Author Response

see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors All comments were addressed.

Author Response

Thank so much you for your important comments that helped me to improve the paper.

Reviewer 2 Report

Comments and Suggestions for Authors

No further comments for the author. 

Author Response

Thank you so much for important comments that helped me to improve the paper.

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors,

I noticed that the typographical error between lines 60 and 61 still persists, although in a different form. At this point, the term appears as an uppercase J in bold, but this literal does not make sense in the context of the equation. It should correctly be written as the subscript JSJ_SJS​.

I recommend carefully checking all equations for similar inconsistencies to ensure clarity and correctness.

Author Response

Thank you so much for your critical comments that helped me to improve the paper.

Agree. I made J_s bold since I was asked to highlight my changings, but that was my bad decision. Sure I will exclude boldness of J and check my calculaions again. Thank you so much for your helpful comments that led to major improvements of my paper.

Reviewer 4 Report

Comments and Suggestions for Authors

The Authors have modified the paper according to the suggestions.

Author Response

Thank you so much for your important comments that helped me to improve the paper.