PONE-D-24-26378Co-infection mathematical model for HIV/AIDS and tuberculosis with optimal control in EthiopiaPLOS ONE

Dear Dr. Ayele,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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ACADEMIC EDITOR:The authors should address the remeaning reviewers' comments. (1) Each section should have its writing aligned.

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We look forward to receiving your revised manuscript.

Kind regards,

Joshua Kiddy K. Asamoah, PhD

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: N/A

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No

Reviewer #2: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: No

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The paper requires a major improvement in order to meet the standards of the journal. My comments are found below.

1. The abstract fails to justify the need for this research study. Also, the first statement in the Abstract is unnecessary. Remove it and reconstruct the abstract with necessary information. Be clear with the reason behind this work, how to go about it and the key results obtained.

2. The novelty of this research is not clearly stated. Please do that.

3. The authors claim that "However, none of these authors have studied the extension of model [68] with HIV/AIDS cohorts and incorporating optimal control efforts". The referred article [68] was extended in 2022 Zhong-Kai et. al. by where the authors studied the HIV/AIDS-TB coinfection model with optimal control by further considering age structure. Authors may find the article details here "Guo, Z. K., Huo, H. F., & Xiang, H. (2022). Optimal control of TB transmission based on an age structured HIV-TB co-infection model. Journal of the Franklin Institute, 359(9), 4116-4137".

4. The authors said also that due to lack of data they picked some parameter values from literature. How true is this? Are the authors claiming that there is no data on HIV/AIDS or TB or their coinfection?

5. In table 2, the authors have indicated that some parameters were fitted. Which year's population for Ethiopia was used for the estimation? Where from the value of N? What is the source of the data used for the estimation? Kindly consider coming out with an updated parameter estimation section.

6. Authors should note that table labels should be placed on top of the table.

7. The article has enormous grammatical errors. Please read through the entire work to correct them.

There are several graphs with no proper discussions on them. Please remove redundant graphs or rewrite the numerical discussions. Numerical simulation discussions should practical.

8. All model assumptions should be supported with literature.

9. Though I see a section on positivity and boundedness. Unfortunately, I did not see any work on positivity. Please provide that.

10. Authors should be clear with the bifurcation analysis. Does the model undergo a forward or backward bifurcation. Where is the bifurcation graph?

11. Under the control model, is early detection not more of a control mechanism than preventive?

12. Conclusion of the work should be updated. The current form is too long and does not highlight the essential aspects of the work. What are the gaps in the work?

13. The introduction and model formulation sections require improvement. Please do that.

Reviewer #2: I read the paper in details, the paper has a potential for publication provided the authors attends to the following suggestions

1. The abstract should contain answers to the following questions: Why is this particular study important? What are the important results from this study different from others? What conclusions can be drawn from the results in this study?

2. The literature review of epidemic models in this direction is too weak and must be improved meticulously, since there are many works in this direction.

3. Support important model assumptions with biological evidences. Also state if the model is a new one or a modification of an existing model.

4. What is the biological significance of the Basic reproduction number, as it regards to disease control? Also discuss Theorem 1 and why it important.

5. What are the epidemiological significance of theorems 1, 2? Be more detailed in discussing the many mathematical analyses. I advise the authors to check some recent papers with useful approach for analysis of stability analysis useful, such as:

a. Mathematical analysis of a novel fractional order vaccination model for Tuberculosis incorporating susceptible class with underlying ailment. International Journal of Modelling and Simulation

b.Mathematical Modelling of Tuberculosis Outbreak in an East African Country Incorporating Vaccination and Treatment. Computation 2023, 11, 143.

c. A mathematical analysis of the two-strain tuberculosis model dynamics with exogenous re-infection. Healthcare Analytics. 4 (2023) 100266

d. A mathematical model for the co-dynamics of COVID-19 and tuberculosis. Mathematics and Computers in Simulation. 27(2023), 499-520

e. . Mathematical model for control of tuberculosis epidemiology. Journal of Applied Mathematics and Computing, (2022)

f. Analysis and Dynamics of Tuberculosis Outbreak: A Mathematical Modelling Approach Advances in System Science and Applications 22(4), 144-161 (2022).

g. Analysis and Dynamics of Tuberculosis Outbreak: A Mathematical Modelling Approach Advances in System Science and Applications 22(4), 144-161 (2022).

and others where detailed discussions have been done for mathematical analysis in epidemiological models. Try and connect your results more to health, in accordance with the scope of the journal.

The Conclusion should be greatly improved and must capture important findings from the study.

Provide detailed future research directions in the conclusion.

The entire manuscript should be thoroughly checked for typos and also the typesetting should be greatly improved to attract wider readership. Make the paper more interesting to readers

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Reviewer #1: No

Reviewer #2: Yes: Olumuyiwa James Peter

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Co-infection mathematical model for HIV/AIDS and tuberculosis with optimal control in Ethiopia

PONE-D-24-26378R1

Dear Dr. Ayele,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Joshua Kiddy K. Asamoah, PhD

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: (No Response)

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: (No Response)

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4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: (No Response)

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: (No Response)

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I have carefully read through the responses and corrections, and I think the authors have accurately responded to my comments. The paper is improved in its current form. Thank you.

Reviewer #2: The authors have addressed all the comments satisfactorily, the manuscript can be accepted in the current form

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: Yes: Olumuyiwa James Peter

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