Mathematical Analysis for Honeybee Dynamics Under the Influence of Seasonality
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors study a disease dynamics for a honey -bee two populations model. The general idea of the proof as well as the tools that they use seem to be appropriate. Nevertheless there are some points that need to be clarified or corrected:
1. Line 94, the disease that is studied is not transmitted by a virus. Bees are not vectors, they are rather treated as target population.
2. Line 156, square matrices F and V are five dimensional while the system has dimension 7. There should be some explanation of this dimension reduction process.
3. The expression for the disease free steady state in line 155 and in line 183 are not consistent. There is some reordering that is not explained.
4. Line 210 and 211: there are two + signs ++.
5. Line 205, Theorem 3 should include in statement explicitly that the hypotheses (A1), (A2), (A3) are assumed.
6. Classical Perron-Frobenius Theorem applies for matrices with non-negative entries, while the authors mention cooperative matrices. Such matrices have positive entries only outside the diagonal, while along the diagonal they have no defined sign. So a Perron-Frobenius result for such matrices should be shown trough a verifiable reference or proved.
6. Line 236, dimension reduction fro 7 to 5 is not mentioned in the time-periodic case. An explanation of this phenomena should be given in comparison with the autonomous case.
7. Line 254 beta_M(t) is not defined and can not be found in any place.
8. Line 278 and 279 m_b(t) is not a matrix it seems that it should say D(t)
Author Response
Please find attached a pdf file with the point-by-point response to the reviewer’s comments.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsReview report is attached
Comments for author File: Comments.pdf
Author Response
Please find attached a pdf file with the point-by-point response to the reviewer’s comments.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsDear Editor, I have read the authors’ manuscript entitled “Mathematical analysis for honeybees’ dynamics under the influence of seasonality” very carefully and I found that their proposed work is interesting and can be considered further for publication; however, I have the following concerns need to be addressed by the authors.
1. What is/are the motivation factor/factors for the authors to propose this study?
2. There are some grammatical errors in the work. Kindly read through the entire paper and correct them.
3. The superiority of the proposed approach must be compared with other established works in the same filed of study.
4. Authors should provide more information about their specific assumptions. Specifically, why this approach is expected to be the best method for investigating such equations. This is very important as anyone in the world who need to reproduce the provided results easily at any time.
5. All the model parameters used to simulate the model are assumed. I know it may be difficult to collect real data, but the authors can take at least took some parameter values from other published sources or will the model be able to stand the test of time? Justify the reason why?
6. Which numerical method used for the numerical simulation of the proposed model? What are the advantages of the selected numerical method? Is there any limitation? Please clarify it.
7. The authors cited references which have similar natures such as 6 and 11; 5 and 7 and finally 12 and 13 please update the reference section of the revised manuscript by citing only 3 of them redundancy is irrelevant.
Author Response
Please find attached a pdf file with the point-by-point response to the reviewer’s comments.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsSome minor corrections to be consiere:
1. Line 150: B_l insetad of F_l in the definition of B
2. Line 158:Explain as in lined 260 why 5-dimensional matrices are considered.
3. Line 179: "then " instead of "therefore".
4. Line 192: \hat{\Sigma} is not defined anywhere.
5. Line 266: \beta_A^+-A_- is not defined
6. Line 281: \phi_A^+-A^- is not defined
7. Line 289-290: In de definition of \Gamma_\partial, there is no explanation of the meaning of Q^p where Q is the Poincaré time T map.
8. Line 393. \mathcal R instead of \mathbb R
Author Response
Thank you for the opportunity to revise our manuscript. We appreciate the careful review and constructive suggestions and comments. We have revised the manuscript accordingly and provided specific answers. Please see the attachment.
Author Response File: Author Response.pdf
