Spatial and Temporal Spread of the COVID-19 Pandemic Using Self Organizing Neural Networks and a Fuzzy Fractal Approach

Round 1

Reviewer 1 Report

I have reviewed the manuscript "Spatial and Temporal Spread of the Coronavirus Pandemic using Self Organizing Neural Networks and a Fuzzy Fractal Approach", Manuscript ID: sustainability-1292603. In this paper, the authors analyze the evolution in space and in time of the coronavirus pandemic by making use of a neural network approach in order to obtain a spatial analysis of data, and of a fuzzy fractal method for gathering the temporal trends of the time series of the analyzed countries. The most relevant contribution highlighted by the authors is the fact that the above-mentioned combined method offers the possibility to help in planning control actions for the coronavirus pandemic.

I consider that the article will benefit if the authors take into account the following remarks and address within the manuscript the signaled issues:

Remark 1: the main strong point of the manuscript consists in the fact that it approaches an interesting and actual topic.

Remark 2: the main weak point of the manuscript under review consists in its devised approach. Taking into account the fact that the initial SARS-CoV-2 virus has mutated over time, resulting in genetic variation in the population of circulating viral strains over the course of the COVID-19 pandemic, I consider that the authors should explain within the paper how did they intend to tackle issues related to the unpredictability of the new SARS-CoV-2 viral mutations that tend to occur more and more frequently.

Remark 3: originality issues. The manuscript under review approaches similar problems tackled in a previous paper, written by the same research team and published in another MDPI Journal, namely the paper "Castillo, O.; Melin, P. A Novel Method for a COVID-19 Classification of Countries Based on an Intelligent Fuzzy Fractal Approach. Healthcare 2021, 9, 196. https://doi.org/10.3390/healthcare9020196". Consequently, the authors have succeeded in establishing a precedence in their line of research. I consider a major omission not to cite the above-mentioned paper. Therefore, I consider that the manuscript under review will benefit a lot if, when discussing their obtained results from the manuscript under review, the authors refer their previous paper and highlight how the timeline of their research has evolved from the findings of their previous study to the present research results reported in the current manuscript. In this context, I would like the authors of the Manuscript ID: sustainability-1292603 to highlight clearly, by writing in the paper, what are the main differences between their conducted study and the previous one and the reason why they have used a large amount of text from the previous paper (including Figures), without citing it. For example, it seems very hard to believe that two different studies, based on two different approaches, are able to forecast identical values, due to the fact that "Figure 15 Forecasting of Belgium confirmed cases from 22 July to 1 August 2020" and "Figure 16 Forecasting of Italy confirmed cases (period of 22 July to 1 August of 2020)" from the manuscript under review, which are identical to "Figure 16. Forecasting the confirmed cases of Belgium from 22 July to 1 August 2020" and "Figure 17. Forecasting Italy confirmed cases from 22 July to 1 August of 2020", from the previous paper. The authors should specify in the manuscript under review that it represents a continuation of their previous study (therefore being mandatory to cite the respective previous paper). In my opinion, presenting a detailed comparison of the approach and the results from the paper under review with the ones from the previous paper is a very important, relevant and mandatory aspect.

If the above-mentioned problems related to the research design and originality issues are solved, I consider that the paper will benefit if the authors address within the manuscript the following aspects:

Remark 4: the "Abstract" of the manuscript. In what concerns the "Abstract", I consider that the authors should structure it as to cover the most important points of interest: the authors should have positioned the manuscript’s topic in a broad context therefore covering appropriately the topic’s background; the authors should have presented succinctly the methods they have employed  in order to attain the purpose of their study; the authors should have summarized the most important outcomes of their study and the conclusions that one could draw. In the actual form of the manuscript, the abstract offers information related only to some of these aspects and even so, their delimitation is unclear.

Remark 5: the gap in the current state of knowledge. After having performed a critical survey of what has been done up to this point in the scientific literature, the authors must identify and state more clearly in the paper a gap in the current state of knowledge that needs to be filled, a gap that is being addressed by their manuscript. This gap must also be used afterwards by the authors, in the final part of the manuscript as well (when discussing the obtained results), where the authors should justify why their approach fills the identified gap in rapport with previous studies from the scientific literature.

Remark 6: the neural network approach. At Lines 70-73, the authors state: "one of the most important contributions of this article is the utilization of neural networks for clustering similar countries with respect to their status in the Coronavirus pandemic, and consequently be able to put forward common strategies for countries in the same cluster". As the authors have used an Artificial Neural Network approach, I consider that the authors must specify in the paper how often does the network need to be retrained/updated and how did they tackle the need of retraining/updating the network. How is the new data encountered stored for subsequent updates of the network? Meanwhile, the paper will benefit if the authors present more details regarding the results obtained during various tests, for all the different number of hidden layers, neurons and epochs tested and especially the training time for each test, until they have obtained the configuration that has provided the best results. The information can be summarized in a table and if it becomes too long, the authors can restrict it in the paper to ten main experimental runs, and a complete table with all the experimental runs can be inserted in the "Supplementary Materials" file of the article.

Remark 7: the flowchart. In addition to the actual explanations, in order to help the readers better understand the methodology of the conducted research, when presenting the devised method in the "Proposed Method" section, it will be extremely helpful to design and insert a diagram, a flowchart depicting the main sequence of steps that one has to process in order to reproduce the results of the conducted study. This diagram should be analyzed in detail within the manuscript by specifying all the elements needed for each and every step, in order to reach the final result of the study.

Remark 8: the details regarding the datasets. At Lines 174-175, the authors state: "The datasets used for all the experiments were collected from the Humanitarian Data Exchange (HDX) [17], which includes worldwide data COVID-19 cases for the countries." I would like the authors to provide in the paper more details regarding the way in which they intend to solve the problems related to missing data or abnormal values if they are to occur. I consider that the exact datasets that the authors have used will be a valuable addition to the article if they are provided as supplementary materials to the manuscript as the authors must provide all the necessary details as to allow other researchers to verify, reproduce, discuss and extend the obtained scientific results based on the obtained published results.

Remark 9: the generalization capability of the developed approach. Can the authors mention how much of their model is being influenced by the used data or to which extent the model can be easily applied to other situations, when the datasets are different? In this way, the authors could highlight more the generalization capability of their approach in order to be able to justify a wider contribution that has been brought to the current state of art.

Remark 10: the comparison between the study from the manuscript with other ones from the literature is missing. After having presented and analyzed the results, the authors should move forward and must devise a comparison between their developed approach and results from the manuscript and other ones from the literature that have been developed and used in the literature for the same or related purposes. The authors should also highlight clearly what are the advantages and disadvantages when comparing their devised study with other studies from the scientific literature. The actual form of the manuscript does not reflect clearly the way in which the obtained approach can be perceived in perspective of previous studies that have tackled similar problems. This comparison is mandatory in order to highlight the clear contribution to the current state of knowledge that the authors have brought.

Remark 11: insight. The paper will benefit if the authors make a step further, beyond their approach and provide an insight when discussing their obtained results regarding what they consider to be, based on the obtained results, the most important, appropriate and concrete steps that all the involved parties should take in order to benefit from the results of the research conducted within the manuscript as to attain the ultimate goal of sustainability.

Remark 12: the "Conclusions" section of the manuscript. In this section the authors should avoid simply summarizing the aspects that they have already stated in the body of the manuscript. Instead, they should interpret their findings at a higher level of abstraction than in the previous sections of the manuscript. The authors should highlight whether, or to what extent they have managed to address the necessity identified within the "Introduction" section (the identified gap). The authors should not restate what they have done or what the article does, they should focus instead on what they have discovered and most important on what their findings actually mean to the scientific community.

Remark 13: the software and the detailed hardware configuration. It will benefit the paper if, along with the elements already presented, the authors specify details regarding the version numbers for the software and the detailed hardware configuration used to obtain the results.

Remark 14: the paper has been submitted to the MDPI Journal Sustainability. As the paper has been submitted to the MDPI Journal Sustainability, I consider that the authors should strengthen the main impact and relationship of their study with regard to attaining sustainability. In the actual form of the paper, this connection is not explicitly mentioned anywhere. It will benefit the paper if the authors provide more details on this issue.

Other Remarks concerning the form.

Remark 15: Section 3, Lines 121-123. At these Lines, the authors state: "This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn". These sentences have nothing to do with the content of the manuscript, they represent some indications from the Sustainability MDPI Journal's Template.

Remark 16: the acronyms used within the manuscript. Line 18: "is proposed for efficient COVID-19 forecasting of the countries." Even if they are widely known, the acronyms used in the manuscript should be explained the first time when they are introduced, for example, in the above-mentioned case, as "Coronavirus disease 2019 (COVID-19)". Please address this issue for all the acronyms.

Author Response

I have reviewed the manuscript "Spatial and Temporal Spread of the Coronavirus Pandemic using Self Organizing Neural Networks and a Fuzzy Fractal Approach", Manuscript ID: sustainability-1292603. In this paper, the authors analyze the evolution in space and in time of the coronavirus pandemic by making use of a neural network approach in order to obtain a spatial analysis of data, and of a fuzzy fractal method for gathering the temporal trends of the time series of the analyzed countries. The most relevant contribution highlighted by the authors is the fact that the above-mentioned combined method offers the possibility to help in planning control actions for the coronavirus pandemic.

R: Thank you for the comments on the paper.

I consider that the article will benefit if the authors take into account the following remarks and address within the manuscript the signaled issues:

Remark 1: the main strong point of the manuscript consists in the fact that it approaches an interesting and actual topic.

R: Thank you for the comment on the strong point of the paper.

Remark 2: the main weak point of the manuscript under review consists in its devised approach. Taking into account the fact that the initial SARS-CoV-2 virus has mutated over time, resulting in genetic variation in the population of circulating viral strains over the course of the COVID-19 pandemic, I consider that the authors should explain within the paper how did they intend to tackle issues related to the unpredictability of the new SARS-CoV-2 viral mutations that tend to occur more and more frequently.

R: Thank you for the comment of the weak point. We agree with the reviewer on the fact we still need to consider the unpredictability of the new viral mutations, and in fact as part of the solution we plan to extend the type of fuzzy logic that was used (that is type-1 in this paper) to type-2, which has more power to manage uncertainty in predicting dynamic processes.

Remark 3: originality issues. The manuscript under review approaches similar problems tackled in a previous paper, written by the same research team and published in another MDPI Journal, namely the paper "Castillo, O.; Melin, P. A Novel Method for a COVID-19 Classification of Countries Based on an Intelligent Fuzzy Fractal Approach. Healthcare 2021, 9, 196. https://doi.org/10.3390/healthcare9020196". Consequently, the authors have succeeded in establishing a precedence in their line of research. I consider a major omission not to cite the above-mentioned paper. Therefore, I consider that the manuscript under review will benefit a lot if, when discussing their obtained results from the manuscript under review, the authors refer their previous paper and highlight how the timeline of their research has evolved from the findings of their previous study to the present research results reported in the current manuscript. In this context, I would like the authors of the Manuscript ID: sustainability-1292603 to highlight clearly, by writing in the paper, what are the main differences between their conducted study and the previous one and the reason why they have used a large amount of text from the previous paper (including Figures), without citing it. For example, it seems very hard to believe that two different studies, based on two different approaches, are able to forecast identical values, due to the fact that "Figure 15 Forecasting of Belgium confirmed cases from 22 July to 1 August 2020" and "Figure 16 Forecasting of Italy confirmed cases (period of 22 July to 1 August of 2020)" from the manuscript under review, which are identical to "Figure 16. Forecasting the confirmed cases of Belgium from 22 July to 1 August 2020" and "Figure 17. Forecasting Italy confirmed cases from 22 July to 1 August of 2020", from the previous paper. The authors should specify in the manuscript under review that it represents a continuation of their previous study (therefore being mandatory to cite the respective previous paper). In my opinion, presenting a detailed comparison of the approach and the results from the paper under review with the ones from the previous paper is a very important, relevant and mandatory aspect.

If the above-mentioned problems related to the research design and originality issues are solved, I consider that the paper will benefit if the authors address within the manuscript the following aspects:

R: We thank the reviewer for the comments. We have now included the mentioned reference of our previous work, along with two other references that could be considered as related. We also discuss in the paper the previous works done and we have described in detail that the present work is a continuation of the previous studies of our research group. In fact, the previous paper on the Healthcare journal was mainly aimed at the classification part of the problem, but we also did show some initial results of prediction, and definitely we were working on the ideas that are now presented in this paper.

Remark 4: the "Abstract" of the manuscript. In what concerns the "Abstract", I consider that the authors should structure it as to cover the most important points of interest: the authors should have positioned the manuscript’s topic in a broad context therefore covering appropriately the topic’s background; the authors should have presented succinctly the methods they have employed  in order to attain the purpose of their study; the authors should have summarized the most important outcomes of their study and the conclusions that one could draw. In the actual form of the manuscript, the abstract offers information related only to some of these aspects and even so, their delimitation is unclear.

R: We thank the reviewer for the comments on the abstract of the paper. Accordingly, we have made every possible effort to structure the abstract in a better way and also summarizing the most important outcomes and conclusions that can be drawn from the study.

Remark 5: the gap in the current state of knowledge. After having performed a critical survey of what has been done up to this point in the scientific literature, the authors must identify and state more clearly in the paper a gap in the current state of knowledge that needs to be filled, a gap that is being addressed by their manuscript. This gap must also be used afterwards by the authors, in the final part of the manuscript as well (when discussing the obtained results), where the authors should justify why their approach fills the identified gap in rapport with previous studies from the scientific literature.

R: We thank the reviewer for pointing out this missing issue in the paper. Accordingly, we are now stating the gap in the current state of knowledge. This is done in the Introduction after stating the existing work in the current literature.

Remark 6: the neural network approach. At Lines 70-73, the authors state: "one of the most important contributions of this article is the utilization of neural networks for clustering similar countries with respect to their status in the Coronavirus pandemic, and consequently be able to put forward common strategies for countries in the same cluster". As the authors have used an Artificial Neural Network approach, I consider that the authors must specify in the paper how often does the network need to be retrained/updated and how did they tackle the need of retraining/updating the network. How is the new data encountered stored for subsequent updates of the network? Meanwhile, the paper will benefit if the authors present more details regarding the results obtained during various tests, for all the different number of hidden layers, neurons and epochs tested and especially the training time for each test, until they have obtained the configuration that has provided the best results. The information can be summarized in a table and if it becomes too long, the authors can restrict it in the paper to ten main experimental runs, and a complete table with all the experimental runs can be inserted in the "Supplementary Materials" file of the article.

R: We thank the reviewer for the comments. Regarding the neural network details, as the network is a self-organizing map (unsupervised network) it does not have hidden layers, it has a very simple structure with only one input layer and one output layer. Both the input and output layers have 199 nodes (this is the number of countries considered in the study) and the number of epochs is 1000. Now this information is included in the paper. Regarding the process of retraining the network we have noticed that both the spatial and temporal changes require at least one month to be noticeable, so this retraining will have to be done again after this period of time. Of course, this is dependent on the changes that are occurring, as it could happen that if the situation is very stable the retraining will not be needed for longer periods of time. In conclusion, we envision in the future another module to our system that could be monitoring the situation to activate the retraining only when the situation will require that.

Remark 7: the flowchart. In addition to the actual explanations, in order to help the readers better understand the methodology of the conducted research, when presenting the devised method in the "Proposed Method" section, it will be extremely helpful to design and insert a diagram, a flowchart depicting the main sequence of steps that one has to process in order to reproduce the results of the conducted study. This diagram should be analyzed in detail within the manuscript by specifying all the elements needed for each and every step, in order to reach the final result of the study.

R: We thank the reviewer for the suggestion. However, we believe that Figure 11 summarizes the whole process occurring in the hybrid model. We can notice in this Figure that there are two flows of information, one going to the SOM model and the other to the fractal model. The same information is used in both models to calculate the classes and fractal dimension, respectively. After this, the two outputs are used as inputs to the fuzzy system, to finally obtain the prediction. If we represent this process in a Flowchart the diagram is very trivial, as there are no decisions to be made. We just have the same data going into two different models, which obtain two different outputs and then we combine them to estimate the final output. We believe the suggestion of the reviewer will be very helpful in the future when we go into the phase of implementing a real time software for users in which there could be choices to make and then the flowchart would be very helpful. We are now mentioning in the paper this future work.

Remark 8: the details regarding the datasets. At Lines 174-175, the authors state: "The datasets used for all the experiments were collected from the Humanitarian Data Exchange (HDX) [17], which includes worldwide data COVID-19 cases for the countries." I would like the authors to provide in the paper more details regarding the way in which they intend to solve the problems related to missing data or abnormal values if they are to occur. I consider that the exact datasets that the authors have used will be a valuable addition to the article if they are provided as supplementary materials to the manuscript as the authors must provide all the necessary details as to allow other researchers to verify, reproduce, discuss and extend the obtained scientific results based on the obtained published results.

R: We thank the reviewer for the comments. We are using the datasets that can be found in [17] and are available to the public, which means that anybody can download the data for the periods that we mention in the paper. We believe that is not needed to repeat the data in the present paper, as the tables are very long and as we have already said the data is available and we have collected exactly as can be found there. Regarding the other comment, which is very interesting, regarding possible missing data, we believe that such uncertainties can be properly handled by the fuzzy model as fuzzy logic is a theory that has as its main aim, modeling and capturing the uncertainty in information and knowledge. In summary, we believe that fuzzy logic is able to manage these issues of missing data or abnormal values.

 

Remark 9: the generalization capability of the developed approach. Can the authors mention how much of their model is being influenced by the used data or to which extent the model can be easily applied to other situations, when the datasets are different? In this way, the authors could highlight more the generalization capability of their approach in order to be able to justify a wider contribution that has been brought to the current state of art.

R: Thank you for the comments. We believe that the proposed model is applicable to other problems as long as they have both temporal and spatial components. We only need to have data from a problem that can be processed both by the self-organizing map and the fractal dimension algorithm and then the proposed hybrid model can provide prediction results. We envision that this proposed model can also be used in prediction economic or financial time series from countries, or similar problems. We are now including the generalization capability in the conclusion section.

 

Remark 10: the comparison between the study from the manuscript with other ones from the literature is missing. After having presented and analyzed the results, the authors should move forward and must devise a comparison between their developed approach and results from the manuscript and other ones from the literature that have been developed and used in the literature for the same or related purposes. The authors should also highlight clearly what are the advantages and disadvantages when comparing their devised study with other studies from the scientific literature. The actual form of the manuscript does not reflect clearly the way in which the obtained approach can be perceived in perspective of previous studies that have tackled similar problems. This comparison is mandatory in order to highlight the clear contribution to the current state of knowledge that the authors have brought.

R: Thank you for the comments. In the new version of the paper, we have now included a new section 7 entitled “Discussion of Results” in which we now discuss the obtained results with the proposed method in comparison with other methods.

Remark 11: insight. The paper will benefit if the authors make a step further, beyond their approach and provide an insight when discussing their obtained results regarding what they consider to be, based on the obtained results, the most important, appropriate and concrete steps that all the involved parties should take in order to benefit from the results of the research conducted within the manuscript as to attain the ultimate goal of sustainability.

R: Thank you for your comments. As mentioned previously, we have added a new section 7 to discuss the results, and also, we have mentioned the relation of the paper to the goal of sustainability.

Remark 12: the "Conclusions" section of the manuscript. In this section the authors should avoid simply summarizing the aspects that they have already stated in the body of the manuscript. Instead, they should interpret their findings at a higher level of abstraction than in the previous sections of the manuscript. The authors should highlight whether, or to what extent they have managed to address the necessity identified within the "Introduction" section (the identified gap). The authors should not restate what they have done or what the article does, they should focus instead on what they have discovered and most important on what their findings actually mean to the scientific community.

R: Thank you for the comments on the Conclusions of the paper. In the new version of the manuscript we have now included more general comments about the proposed model and the obtained results.

Remark 13: the software and the detailed hardware configuration. It will benefit the paper if, along with the elements already presented, the authors specify details regarding the version numbers for the software and the detailed hardware configuration used to obtain the results.

R: Thank you for the comments of missing software and hardware information. In the new version of the paper we have now included details about the used software and hardware. These details can be found at the beginning of Section 6.

Remark 14: the paper has been submitted to the MDPI Journal Sustainability. As the paper has been submitted to the MDPI Journal Sustainability, I consider that the authors should strengthen the main impact and relationship of their study with regard to attaining sustainability. In the actual form of the paper, this connection is not explicitly mentioned anywhere. It will benefit the paper if the authors provide more details on this issue.

R: Thank you for the comment regarding the relation of the paper to the sustainability issue. In new version of the paper (In the Introduction) we have added an explanation of this issue.

Other Remarks concerning the form.

Remark 15: Section 3, Lines 121-123. At these Lines, the authors state: "This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn". These sentences have nothing to do with the content of the manuscript, they represent some indications from the Sustainability MDPI Journal's Template.

R: Thank you for point out this typo in the paper. It was originated when using the template to convert the format of the manuscript to the format of papers in the journal. We have now fixed this issue in the new version of the paper.

Remark 16: the acronyms used within the manuscript. Line 18: "is proposed for efficient COVID-19 forecasting of the countries." Even if they are widely known, the acronyms used in the manuscript should be explained the first time when they are introduced, for example, in the above-mentioned case, as "Coronavirus disease 2019 (COVID-19)". Please address this issue for all the acronyms.

R: Thank you for indicating this issue with the paper. We have now fixed this issue in the new version of the manuscript. Accordingly, we have now defined all acronyms the first time they appear in the manuscript.

Reviewer 2 Report

The paper is presented reasonably well but I have a few concerns:

• The paper seems not to have any significant innovation and I'm under the impression that is the result of a combination of two standard methods. The authors should clarify their innovations at least with a bullet list.
• How does spatiality enter your analysis? I get that you identify the clusters that you later use, but I don't understand how this takes into account the spatial dimension, to me it seems another temporal analysis (the clusters are obtained from COVID cases data, that somehow have temporal information in them) or at most an individualized (based on clusters) system identification technique to obtain better predictions.
• The self organising NN seem to be overkill for the task. A lot of simpler classifiers (NN or not) can be made with the same goal (at the end of the day, you obtain a 4 level quantization starting from data that can be encoded in a curve...wouldn't studying the derivatives or other features of the curves suffice?).
• The fuzzy system also appears to be an overkill solution and the fact that its rules come from some heuristic analysis on historical data is not reassuring.
• The results are discussed over a few days that show basically a linear behaviour, and this makes me think that the problem at hand, for how it was formulated, can be solved with a much simpler solution. I don't think that the paper
• The simulations need a benchmark solution to compare against
• the authors do not clearly provide all data and parameters to repeat the simulations.

Author Response

The paper is presented reasonably well but I have a few concerns:

• The paper seems not to have any significant innovation and I'm under the impression that is the result of a combination of two standard methods. The authors should clarify their innovations at least with a bullet list.

R: Thank you for the comments. We do not agree with the reviewer regarding “no significant innovation” as the proposed approach is combining three methods, which has not previously done in the literature, in this case the self-organizing maps, fuzzy logic and fractal methods, for spatial and temporal analysis of data and its application for time series prediction. We have now included in the new version of the paper a more detailed explanation on the innovation of the approach.

• How does spatiality enter your analysis? I get that you identify the clusters that you later use, but I don't understand how this takes into account the spatial dimension, to me it seems another temporal analysis (the clusters are obtained from COVID cases data, that somehow have temporal information in them) or at most an individualized (based on clusters) system identification technique to obtain better predictions.

R: Thank you for your comments. The idea of using the spatial analysis is to group similar countries (in this case, according to COVID data) and later this information is used as input in the fuzzy rules to help perform a prediction for the countries. In this form, for example, countries that are the class “high” are forecasted similarly. The fuzzy rules of the fuzzy system also use the fractal dimension as a measure of the complexity of the time series of the countries.

• The self organising NN seem to be overkill for the task. A lot of simpler classifiers (NN or not) can be made with the same goal (at the end of the day, you obtain a 4 level quantization starting from data that can be encoded in a curve...wouldn't studying the derivatives or other features of the curves suffice?).

R: Thank you for the comments. We do not agree with the reviewer that the SOM is an overkill, as we are proposing a hybrid intelligent approach that, in theory could be applied for more complex problems, so that the use in general is also important. We have included some comments about the general usability of the proposed approach.

• The fuzzy system also appears to be an overkill solution and the fact that its rules come from some heuristic analysis on historical data is not reassuring.

R: Thank you for the comments. We do not agree with the reviewer that the “fuzzy system is an overkill”, as the advantage of using a fuzzy system instead of a mathematical model is that we can encapsulate knowledge of experts and also we can model the uncertainty of the data, so we have a more powerful representation of the problem and potentially a better prediction by using fuzzy logic. We have now included comments about this in the paper, so that it can clearer for the readers.

 

The results are discussed over a few days that show basically a linear behaviour, and this makes me think that the problem at hand, for how it was formulated, can be solved with a much simpler solution. I don't think that the paper

R: Thank you for the comments. We have tested the proposed approach with a specific period of time in this paper, but we plan to extend the periods of time and consider new periods and other countries. We also plan in the future to consider other problems (different than COVID-19 problem) to explore the potential usability of the proposed approach.

 

• The simulations need a benchmark solution to compare against

R: Thank you for the comments. In the case of real COVID-19 data, most of the papers being published at the moment are using the real data to validate the models. The process is as follows, a set of data is divided into training data and testing data. So, the model is formed with the training data and then is validated with the testing data, which was not seen by the model.

 

• the authors do not clearly provide all data and parameters to repeat the simulations.

R: We thank the reviewer for the comments. We are using the datasets that can be found in [17] and are available to the public, which means that anybody can download the data for the periods that we mention in the paper. Regarding the parameters of the SOM neural network, we are now providing the parameters needed to repeat the simulations.

 

Reviewer 3 Report

The authors propose a strong application paper on modeling in the context of the pandemic situation. The combination of self organizing neural networks and fuzzy fractals is used and appreciated.

The paper is actual and also important.

The theory is correct. The application is also correct and very illustrative.

 

Author Response

The authors propose a strong application paper on modeling in the context of the pandemic situation. The combination of self organizing neural networks and fuzzy fractals is used and appreciated.

R: Thank you for the positive comments on the paper, which are very encouraged by your words to continue our research work.

 

The paper is actual and also important.

R: Thank you for the comment on the paper.

 

The theory is correct. The application is also correct and very illustrative.

R: Thank you for the comments on the paper.

Reviewer 4 Report

This study assesses the spatial and temporal evolution of the COVID-19 pandemic with self-organizing neural networks and a fuzzy fractal approach. In contrast with most of the existing COVID-19 studies, this study analyzes a spatial evolution of the COVID-19 pandemic. Moreover, self-organizing neural networks and the fuzzy fractal approach are combined for evaluation and forecasting purposes. This study possesses significant merit. However, it has a few shortcomings as follows:

- Contributions of a paper are generally not highlighted in the abstract. So, it is advised to remove or modify the last sentence in the abstract (“The most relevant contribution …”). Contributions should be clearly outlined by the end of the introduction section.
- The description of self-organizing neural networks, especially layers, could be more vivid.
- Section 5 includes some methods that were not developed by this study (e.g., Mamdani reasoning scheme, centroid method). References for such methods should be provided.
- The manuscript includes several grammatical and punctuation errors that need to be fixed. Furthermore, there are some long sentences without commas, which are hard to follow.
- Some of the figures (e.g., Figure 3) do not have a good resolution.

Author Response

This study assesses the spatial and temporal evolution of the COVID-19 pandemic with self-organizing neural networks and a fuzzy fractal approach. In contrast with most of the existing COVID-19 studies, this study analyzes a spatial evolution of the COVID-19 pandemic. Moreover, self-organizing neural networks and the fuzzy fractal approach are combined for evaluation and forecasting purposes. This study possesses significant merit. However, it has a few shortcomings as follows:

R: Thank you for the comments on the paper. We have made every possible effort address the shortcomings pointed out by the reviewer and the replies are presented below.

 

- Contributions of a paper are generally not highlighted in the abstract. So, it is advised to remove or modify the last sentence in the abstract (“The most relevant contribution …”). Contributions should be clearly outlined by the end of the introduction section.

R: Thank you for the comments. We have improved the abstract of the paper, as well as the introduction, and hopefully the contribution is now better explained in the introduction section.

- The description of self-organizing neural networks, especially layers, could be more vivid.

R: Thank you for your comments. We have now provided more information on the self-organizing neural networks. Hopefully, this is now more acceptable for the reviewer.

- Section 5 includes some methods that were not developed by this study (e.g., Mamdani reasoning scheme, centroid method). References for such methods should be provided.

R: Thank you for the comments. We have made reference to some original works in fuzzy systems in Section 4, where the basic concepts of fuzzy logic are briefly discussed.

- The manuscript includes several grammatical and punctuation errors that need to be fixed. Furthermore, there are some long sentences without commas, which are hard to follow.

R: Thank you for the comments. We have made every possible effort to fix the grammatical and punctuation errors. In addition, we fix some long sentences by adding commas.

- Some of the figures (e.g., Figure 3) do not have a good resolution.

R: Thank you for the comments. We have made every possible effort to improve the resolution of the Figures.

Round 2

Reviewer 1 Report

I have reviewed the manuscript "Spatial and Temporal Spread of the Coronavirus Pandemic using Self Organizing Neural Networks and a Fuzzy Fractal Approach", Manuscript ID: sustainability-1292603 that has been submitted for publication in the Sustainability MDPI Journal and I can conclude that the authors have addressed most of the signaled issues, therefore improving the manuscript.

Reviewer 2 Report

the replies are reasonable and I have no other comments