Modeling the Impact of the Imperfect Vaccination of the COVID-19 with Optimal Containment Strategy
Round 1
Reviewer 1 Report
After reviewing the document, I consider it to be a study of very high quality that shows that through mathematical models it is possible to help see the problem in a population with respect to the population, as well as improve vaccination campaigns after analyzing the results with different methods. that foresee different scenarios and opt for the most appropriate according to the characteristics of the population under analysis, could help improve global vaccination and get ahead more quickly in this pandemic
I consider it to be an excellent study that should be published.
Author Response
Dear Reviewer,
we would like to thank your for your valuable comments that help to improve the quality of our work. An acknowledgment to your effort was added at the end of the paper.
All the changes, requested by the reviewer, are made in blue.
Please notice that per one of the reviewers recommendation, we slightly change the title of the paper “Modeling the Optimal Vaccination Strategies for COVID-19 in Morocco ” to “Modeling the impact of the imperfect vaccination of the COVID-19with optimal containment strategy”
We are looking forward to hearing from you.
abdessamad tridane
Author Response File: 
Author Response.pdf
Reviewer 2 Report
It is a very interesting and a very well written paper. I very much like the discussion on the 4 cases/scenarios and the direct follow up in the form of an advise for the policy-makers. That being said, I would suggest that the authors make some really minor aesthetic edits on their work so that it gets more attention. Specifically,
- Please, expand the abstract so that the notion of the four scenarios and policy-advise come to the surface of your discussion.
- Please, consider using the word scenario, instead of case, it it will be more representative.
- Please, consider editing the title of your paper to depict the practical aspect of your work.
- Please, carefully read the whole paper to address this kind of style issues as this one (lines 260-262): "To investigate further the possible 260 additional measures that help with vaccination [a coma should be added here] we introduce an optimal control problem with the 261 goal of increasing the awareness of vaccination, limiting the probability of infection by adhering to a 262
preventative protocol and increasing the efficacy of the vaccine. T
Author Response
Dear Reviewer,
Please find enclosed a revised version of our paper manuscript axioms-1579100, the authors: Lahbib Benahmadi , Mustapha Lhous , Abdessamad Tridane , Omar Zakary and Mostafa Rachik, which we would like to submit as a Research paper for the Special Issue "Calculus of Variations,Optimal Control, and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of his 50th Birthday"
Per the reviewer recommendations, we slightly change the title of the paper “Modeling the Optimal Vaccination Strategies for COVID-19 in Morocco ” to “Modeling the impact of the imperfect vaccination of the COVID-19with optimal containment strategy”
In this revised version, we made sure that the reviewers can track all the changes that we made, as we have the revised part in blue color.
We would like to thank you for your inputs and comments that help to improve the quality of our paper. An acknowledgment was added at the end of the paper for this purpose.
Considerations
Author Response File: Author Response.pdf
Reviewer 3 Report
The article is devoted to an important and relevant topic.
However, there are a number of remarks, the elimination of which will improve the quality of work.
1. Explanations are needed for all variables that are used in the right parts of equations (1). What is SE, SI, VE, VI, etc.? Obviously, these are products of variables? There are a lot of variables in the article as a whole. I propose to additionally make their description in a separate section.
2. What does just sigma mean in line 78 if 1/sigma is the length of the quarantine and hospitalization periods?
3. In line 80 N(t)=N? Is this the same N that is in the denominator of formulas (1)? In what range can alpha, beta, gamma, sigma change?
4. Link to fig. 1 is missing. The quality of this drawing needs to be improved.
5. In line 86 there should be a comma instead of a period before the word "then", after which a comma is not needed!
6. The formula before line 89 does not fit in its own line! Formula (2) is followed by X(t) = [S(t), V(t), E(t), I(t), Q(t), H(t), C(t), R(t ), D]. This should be D(t).
7. It is necessary to indicate for F(x) all 9 elements on page 4 in the explanations to the formula (2).
8. Why D(X) = AX + F(X)? What is D(X)? We already have one D(t).
9. Need clarification on the used vectors F, V in the second paragraph on page 5. Why are the matrices what the asterisks mean?
10. Why are the matrices (F and F) labeled the same in line 100? Show that there is a dependency on Xj for F, V.
11. Show why such a formula (3).
12. Formula (5): Is this an equation if there is no "=" sign?
13. On line 111: is this an equation?
14. Line 111 is very bad with English!
15. On page 6 in the fourth inequality from the top: why is there "+-" here? After "From the previous equation (7) if R0 < 1 then", "Using the same steps, from the equation (7) if R0 > 1 then".
16. In line 116, set the equation to zero.
17. Why in line 119 "Where" is a capital letter c (and before it - a dot)?
18. There must be a description of all variables and constants somewhere (page 8).
19. What does the subscript "ad" mean in line 136, 139?
20. Not correct in English: "There exists an optimal control..."
21. It is necessary to say what the elements of the vector are measured in lines 175, 176.
22. Poorly written in terms of English in line 181 (we get...)
23. On line 185: what exactly is the sensitivity index? 24. Correct designations in the first column of table 1.
25. Why such strange references to tables and figures (in parentheses (line 200)).
26. Figures 3-7 need to be scaled up.
Author Response
Dear Reviewer,
Please find enclosed a revised version of our paper manuscript axioms-1579100, the authors: Lahbib Benahmadi , Mustapha Lhous , Abdessamad Tridane , Omar Zakary and Mostafa Rachik, which we would like to submit as a Research paper for the Special Issue "Calculus of Variations,Optimal Control, and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of his 50th Birthday"
Per the reviewer recommendations, we slightly change the title of the paper “Modeling the Optimal Vaccination Strategies for COVID-19 in Morocco ” to “Modeling the impact of the imperfect vaccination of the COVID-19with optimal containment strategy”
In this revised version, we made sure that the reviewers can track all the changes that we made, as we have the revised part in blue color.
We would like to thank you for your inputs and comments that help to improve the quality of our paper. An acknowledgment was added at the end of the paper for this purpose.
Considerations
abdessamad tridane
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The paper can be published in present form.
