Optimal Containment Control Strategy of the Second Phase of the COVID-19 Lockdown in Morocco

Round 1

Reviewer 1 Report

In this paper, the authors introduce an epidemic SEIRQ model that describes the spreading of the novel coronavirus infection and the lockdown measures in Morocco. The topic of this paper is very interesting, and a lot of quality work was done in analyzing the parameters of the COVID-19. The authors also present an optimal control structure using the Pontryagin’s maximum principle. The paper is organized very well, and it is really helpful to see the numerical simulation. I recommend that article for publication if the authors change a couple of minor things:

1. Line 11. The Introduction section is repeated twice, but the first time it is completely empty.
2. Line 50. Not a serious remark. You have a Dead subgroup, so it might be better to call the model SEIRQD?
3. Line 50 and so on. Stylistically, it looks better when there is a semicolon at the end of the equation.
4. Line 64. Should there be “fraction” instead of “faction”?
5. Line 74. Should there be “do not have” instead of “to not have”?
6. Lines 77, 84, 113, 116, 162, 166, 193, 211. I do not think this is a big mistake, but stylistically, it seems better to put a space between “Fig.” and a number.
7. Line 80. On this line and beyond, there are sometime large gaps in the article. Maybe there is an option to somehow redistribute the text and images to remove them?
8. Line 83. “When” instead of “where”.
9. Line 90. Stylistically, it is better to write word “table” with a capital letter.
10. Line 105. Figure above does not have a caption and number that is why there are question marks on that line.
11. Lines 107, 108, 109. I do not think this is a serious mistake, but the sentences repeat themselves, and there may be a way to write them differently.
12. Line 125. Starting from this point, there is a problem with line numbering. I also do not think this is a mistake or typo, but it is harder to describe correct line.
13. Line 125. On the sixth line of that paragraph, you consider three variables u, v, and T, so there should be “...we consider the variableS (u_i,v_i,T_i)...”.
14. Line 126. Right before the third formula. I think it is better to write “between the susceptible, the infected, and exposed” instead of “between the susceptible and the infected and exposed”.
15. Line 158. There is only one table in Table 2, so I think on that line should be “see Table 2” instead of “see Tables 2”.
16. Line 163. Stylistically, it is better to write the letters u and v in italics, since you did this everywhere in the previous places.
17. Line 170. Stylistically, it is better to write “i.e.” instead of “ie”.
18. Line 174. I am not sure about this, since I am not a native speaker, but it seems to me that the second "To" is superfluous here. The one before “1800 cases”.
19. Line 182. Again not completely sure, but it seems like it should be “non-control” instead of “non control”.
20. Line 188. Seems like there is a missed space between “by” and “April”.
21. Line 189. There are doubts, but perhaps “of” is unnecessary here.
22. Line 191. Again, there are doubts, but I think it is correct to write “on the day 8 (12)”.

Author Response

We would like to thank the referee for her/his comments that helped us to improve the quality of our work.

The responses to comments are in the attached report

Author Response File: Author Response.pdf

Reviewer 2 Report

Summary

The authors proposed the optimal strategy to lockdown during the COVID-19 in Morocco and validated their discrete epidemic model by fitting the model to the COVID-19 data in the period between April 6 and April 25, 2020. The authors also investigated the impact of optimal control strategies on this pandemic in Morocco. The reported work added the valued knowledge to the field, but the authors should invest more energy to content organization, manuscript writing and proof-reading before the next submission as there are lots of typos of texts, numbers in the current version of the manuscript.

Major comments

1. The organization of the manuscript is poor. The authors should add section Materials and Methods, Results and Discussion, Conclusion, to include an group all relevant contents in each of these sections, respectively.
2. In section Conclusion, authors should summarize and present their conclusions and claims.

Minor comments

1. Please remove Line12, ‘2. Introduction’, and change the section numbers in the manuscript accordingly.
2. Line22-24, please re-write the sentence, ‘Chen et al. … respectively’, to make it clear for readers.
3. The first figure on page6 needs a figure number and title as well as the legend.
4. The second figure (Figure 3) on page6 should be Figure 4 as the first figure on the same page is Figure 3. The figure legend is needed to tell readers which sub-figure represents Active infected cases, Recovered individuals and dead individuals, respectively.
5. Change the figure numbers and relevant texts in the manuscript accordingly (see minor comment 3 and 4) when necessary.
6. The Figure 3. Residual on page6, please add a detailed legend for the figure.
7. Line112, please replace ‘removed’ with ‘recovered’ in the sentence ‘the residuals of the infected, removed and dead populations for data of Morocco’.
8. Line118-120, please provide more details on why authors can claim that, ‘These figures show that the estimated parameters are reliable and predict correctly the observed data of Morocco, especially the number of infections and deaths’.
9. Page12, please add the legend for Figure 5 to describe each sub-figure.

Author Response

We would like to thank the referee for her/his comments that helped us to improve the quality of our work.

The responses to comments are in the attached report.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors did good job to improve the manuscript though I suggest authors to invest more energy on figure legend when they submit a scientific paper to high-rank journals. I just have a few minor comments.

Minor comments:

1. Page12, Figure 6, I would suggest use ‘Evolution dynamic’ instead of ‘Evolutionary dynamics’ if there is no strong reason to use ‘Evolution dynamic’.
2. In the first sight of the revised manuscript, the authors can do their job better in writing detailed figure legends, though the current version is just OK for the publication this time.

Author Response

The authors did good job to improve the manuscript though I suggest authors to invest more energy on figure legend when they submit a scientific paper to high-rank journals. I just have a few minor comments.

We Would like to thank the reviewer for the effort to read our paper carefully. An acknowledgment is added to the paper to recognize this effort.

Minor comments:

1. Page12, Figure 6, I would suggest use ‘Evolution dynamic’ instead of ‘Evolutionary dynamics’ if there is no strong reason to use ‘Evolution dynamic’.

Done

1. In the first sight of the revised manuscript, the authors can do their job better in writing detailed figure legends, though the current version is just OK for the publication this time.

We do not see any issues with the figures’ legends because we made sure to have clear explanations right after each figure. However, we improved it as the reviewer suggested.