A Mathematical Model for the Treatment of Melanoma with the BRAF/MEK Inhibitor and Anti-PD-1

Round 1

Reviewer 1 Report

The article is devoted to developing a new personalized protocol for treating melanoma, combining biological therapy with immunotherapy, described by a mathematical model. The mathematical model contains analytical functions that depend on parameters and variables that can be changed so that the time of administration of the drug and its dose can be controlled. Using analytical functions, the authors propose a new approach to treating melanoma with a BRAF/MEK 1 and anti-PD-1 inhibitor. These functions depend on the time interval and different dosages of drugs. These variable parameters can be adapted to the patient, i.e., personalized treatment. In the current study, the authors show that changing and combining these two parameters simultaneously makes it possible to obtain a reduction in tumor volume.

Despite the satisfactory quality of the article, some shortcomings need to be corrected.

1. The abstract should be expanded with straightforward actuality and results obtained within the research.
2. The aim of the paper should be defined.
3. Formulas are parts of the sentence. The punctuation should be corrected.
4. The mathematical formulation should also be described in the text in more detail.
5. Figures should be interpreted in the text in more detail.
6. The obtained results should be compared with other research.
7. The authors' contribution to the field should be highlighted.
8. The scientific and practical novelty of the research should be highlighted.

In summarizing my comments, I recommend that the manuscript is accepted after major revision, including the presentation of the material. 

Author Response

Please see the attache file

Author Response File: Author Response.pdf

Reviewer 2 Report

I understand that the work is interesting and very important, very well written, however, there is one thing that bothered me: since it is such important work and it uses numerical tools, it is extremely important to validate the numerical results from a numerical precision analysis that is not presented in the text.

Furthermore, I suggest:

- I guess that the excerpt "... of treatment using the functions "(21)" and "(21)" ... " has something is mistakes (lines 122-123);

- Put a color legend in Figure 9 and the vertical axis;

 

- In line 155, correct for: " ... 10 month";" for line 8: 1. ... "

Author Response

please see the attached file with our response to the reviewer's comments. 

Author Response File: Author Response.pdf

Reviewer 3 Report

In this manuscript, the authors proposed a mathematical model for personalized therapy of melanoma using BRAF/MEK inhibitors and anti-PD-1 antibodies. The variables in the model included drug doses, cell density, cytokine levels, etc., which are all critical factors determining the effectiveness of therapies. The model is interesting, and a comparison between this model and a conventional method will enhance the significance of the study. In addition, the Abstract needs to be rewritten to explain the importance of the study, and English needs to be edited throughout the manuscript.

Author Response

Please see the attached file with our answers to the comments. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Thanks for the authors for their analysis and considering some of the reviewers' comments and recommendations. However, some drawbacks should be still corrected:

1. The results of the research should be compared with other researches.

2. Formulas are parts of the sentences. The punctuation should be corrected accordingly.

Author Response

We went through the article again and corrected all the errors. We hope that now all corrections have been made.
Thank you very much and we really appreciate the hard work of the reviewers. 

Reviewer 2 Report

The authors made the corrections conform to what was solicited.

Author Response

The reviewer commented: "The authors made the corrections conform to what was solicited."