Analyzing the Data of COVID-19 with Quasi-Distribution Fitting Based on Piecewise B-Spline Curves

Round 1

Reviewer 1 Report

The paper is devoted to the development of the method of the construction of piecewise quasiuniform B-spline curves modeling the density probability function. This method was applied to COVID-19 data. Comments:

1.  Truly speaking the significance of the results of the work is unclear. It is unclear, how to apply such modeling.  Please describe it. It allows us to predict the random value of the number of infected persons better than it allows us the density probability function (without B-splines). Clarify it.
2. Related works should be better presented. For example, most of the works on COVID-19 epidemiological modeling is dealing with population dynamics. E.g., doi: 10.1109/ACCESS.2021.3104519   or 10.1007/s11071-020-05863-5
3. Why do you divide intervals into 15 subintervals? Some evidence should be added.
4. The conclusion should be extended with some discussion.
5. Labels for all figures should be added. Ar least labels for x axis.
6. Expression (5) should be changed. It is better to use $\arg \min$ in this expression 

Author Response

1) Our research can be considered as the first step towards building, in the long term, a mathematical method to calculate and forecast for the next moment in time. And it showing the declining of the fatality rate, which is proved by nowadays scenario caused by Omicrion.

2) Our research is using a new way to evaluate COVID-19, so we didn't using population dynamics in most of the research paper about COVID-19.

3) Actually we divided the interval of [0,1] into ten subinterval, and the number 15 is related to the number of basis function of 5-order qusi-uniform B-spline curves, but actually it should be 14, because in B-spline curves we usually denote the first basis function as 0, so from 0,1,2...to 14, it's totally 15 basis function, and we already corrected in the new edition, we thank for the reviewer to pointed it out, even though not in the correct way, but anyway, thanks a lot.

4) Our research works debating the results cautiously because we using the data of 500 days, which is ended at the July of 2021, but apparently nowadays scenarios caused Omicron supported our results strongly, but our research didn't containing that data, so we didn't give strong conclusion, but in our next paper, we will.

5)  When we doing our research works, we using VC++ to write the code step by step to doing the fitting process, and the showing of the results are all gotten from the program we made by VC++, as the corresponding author, I have to say our supporting fund is very little, we can't afford those fabulous software to draw beautiful image, but, we add a paragraph (marked in red) before Fig.1 to demonstrate the coordinate in the figures.

6) We type the expression with math-type, it's a little difficult to combine math-type equation with text symbol together.

All the author of this paper would like to thank for the reviewer's careful and rigorous review and would like to say happy new year to you and your family! Hope we would have a fresh new 2022, and of course hoping the pandemic of COVID-19 will come to an end! 

 

 

Reviewer 2 Report

Review of the article - covid-1496264

Analyzing the Data of COVID-19 with Quasi-Distribution

Fitting Based on Piecewise B-spline Curves

Qingliang Zhao2; Zhenhuan. Lu; Yiduo1. Wang1,a*

In this paper, the authors propose an analysis of the development of coronavirus disease in 2019 (COVID-19) using the fitting method (QDF, quasi-distribution), based on piecewise quasi-homogeneous B-spline curves. Numerical experiments based on data from individual countries have shown that the QDF method demonstrates the internal characteristics of the COVID-19 data of a given country or district. Graphical interpretation of the result shows that it is effective and feasible as an evaluation method. A detailed study of the work allows you to note:

1. The results of the work only state statistical data. Research can be considered as the first step towards building, in the long term, a mathematical model that would make it possible to calculate and forecast for the next moment in time.
2. The paper provides data on the disease for a short period of time in Table 1. Table 2 shows only the time period without the statistical data themselves, but at the same time a graphical interpretation of piecewise quasi-homogeneous B-spline curves is given. It is desirable to expand Table 2 with statistical data, but at the same time consider only a few countries in order to avoid a large amount of data.
3. All drawings require improvement in the designation of the coordinate axes. If the text of the work was about probability, then how does the dimension appear on the coordinate axis as a percentage (%).
4. The numbering of formulas is located close to the formulas themselves.

Заключение.

Для публикации материалов необходимо исключить замечания пунктов 2, 3 и 4.

Рецензент.

 

Comments for author File: Comments.pdf

Author Response

1) yes, our work is the first step to build a long term mathematics modeling about coivd-19.

2) The short period time (5 days) in table 1, just demonstrated why we need to use 7-days moving average of the data instead of the original data; because in our paper, for every country we using 500 day's data, so table 2 just show the beginning date and the ending date of every countries' data.

3) When we doing our research works, we using VC++ to write the code step by step to doing the fitting process, and the showing of the results are all gotten from the program we made by VC++, as the corresponding author, I have to say our supporting fund is very little, we can't afford those fabulous software to draw beautiful image, but, we add a paragraph(marked in red) before Fig.1 to demonstrate the coordinate in the figures. And talking to the percentage %, it is because, the scale mark on the longitudinal axis should be 0.0033, 0.0067 and 0.01, we made them to 0.33%, 0.67% and 1% correspondingly to save the space in the figures. 

4) We would thank for the reviewer to point out that the number of formulas was located too close to the formulas themselves, we had corrected in the new edition.

All the author of this paper would like to thank for the reviewer's careful and rigorous review and would like to say happy new year to you and your family! Hope we would have a fresh new 2022, and of course hoping the pandemic of COVID-19 will come to an end! 

Round 2

Reviewer 1 Report

All my comments have been addressed. I recommend the paper for publication

Author Response

the authors would like to thank the reviewer's suggest and changed the language of our paper.

Author Response File: Author Response.docx