Fractional order SEIQRD epidemic model of Covid-19: A case study of Italy

Subrata Paul; Animesh Mahata; Supriya Mukherjee; Prakash Chandra Mali; Banamali Roy

doi:10.1371/journal.pone.0278880

Peer Review History

Original SubmissionJune 12, 2022
6 Jul 2022 Decision Letter - Mohammed S. Abdo, Editor PONE-D-22-16861Fractional order epidemic model of Covid-19: a case study of ItalyPLOS ONE Dear Dr. Mahata, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. ============================== 1) Authors should be prepared to incorporate major revisions. 2) Authors should submit a list of responses to the comments and highlight them in revised manuscript. 3) Authors should avoid citing references that are not relevant to the research topic ============================== Please submit your revised manuscript by Aug 20 2022 11:59PM. 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Additional Editor Comments: Dear Authors, we have received the reports from our advisors on your manuscript "Fractional order epidemic model of Covid-19: a case study of Italy" (PONE-D-22-16861) which you submitted to "PLOS ONE". Based on the advice received, I have decided that your manuscript could be reconsidered for publication should you be prepared to incorporate major revisions. When preparing your revised manuscript, you are asked to carefully consider the reviewers' comments which can be found in the system, and submit a list of responses to the comments and highlight them in revised manuscript. Important note: The authors should not take into account references suggested by reviewers, except for only references that are closely related to the article. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes Reviewer #2: Yes Reviewer #3: Yes ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes Reviewer #3: Yes ****** 3. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes Reviewer #2: Yes Reviewer #3: Yes ****** 4. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes Reviewer #2: Yes Reviewer #3: Yes ******** 5. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: The presentation should be improved. Introduction need attention. Some recent work on COVID-19 relevant to this paper should be cited like: Chaos, Solitons & Fractals 157 (2022): 111955,Results in Physics 19 (2020): 103510.Alexandria Engineering Journal 59.5 (2020): 3221-3231.Results in physics 19 (2020): 103560.Results in Physics (2022): 105649 Reviewer #2: After reading this paper in detail, this paper needs to be revised via follows: The Abstract should contain answers to the following questions: What problem was studied and why is it important? What methods were used? What are the important results? What conclusions can be drawn from the results? What is the novelty of the work and where does it go beyond previous efforts in the literature? [12-16] these paper should be written in clearly "4.3 The Equilibrium Points of the system" this part of the paper needs to be extended a little more. They need to present more information about the novelty of this paper. What is the main contribution of this paper when we compare it via follows DOI:10.1080/17455030.2022.2075954; Modified Predictor–Corrector Method for the Numerical Solution of a FractionalOrder SIR Model with 2019-nCoV; Symmetry, 13(2428), 1-18, 2021;Chaos, Solitons and Fractals, 158(112050), 1-6, 2022; DOI:10.1142/S1793962323500083? What is the advantage of this operatır used in this paper? For this chapter of the paper "4.2 Non-negativity and boundedness of proposed model", they didnt cite any paper. Thus, they need to cite at least one paper related to this part of the paper. After these modifications, this paper may be accepted. Reviewer #3: Reviewer Report on: Title: Fractional order SEIQRD epidemic model of Covid-19: a case study of Italy Journal: PLOS ONE Manuscript ID: PONE-D-22-16861 Authors: Mahata et al. Overall Comments: The authors have examined the fractional order SEIQRD compartmental model in a fractional order framework to account for the uncertainty caused by the lack of information regarding the Coronavirus (COVID-19). In addition, the fractional-order Taylor’s approach is utilized to approximate the solution to the proposed model. The model’s validity is demonstrated by comparing real-world data with simulation outcomes. Furthermore, the system’s analysis and numerical findings show that regular usage of face masks can help to reduce the COVID-19 epidemic. However, it needs some revisions from the point of authors and readers to improve the quality of the paper. After these MAJOR REVISIONS, I suggest that this paper can be accepted to publish in ” PLOS ONE”. My comments are as follows: 1. Ensure the end of each line of the equations has a punctuation, either a comma or a full stop if it is the end of the equation - these are missing in several of the equations, see for example: 2. The Introduction should make a compelling case for why the study is useful along with a clear statement of its novelty or originality by providing relevant information and providing answers to basic questions such as: • What is already known in the open literature? • What needs to be done, why and how? 3. Clear statements of the novelty of the work should also appear briefly in the Abstract and Conclusions sections. 4. How did they decide the Lyapunov function in the global stability analysis? 5. How did they decide determining the initial conditions? 6. What about the parameter values in the system. Where they have been taken them from? 7. Whay did they ignore the fractional order in the system? Is it dimentionally correct now? Discuss the system by comparing the following literature. • Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom. Chaos, Solitons & Fractals, 111954, (2022). • Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey. Computers in biology and medicine, 105044, (2021). 8. What is the main motivation in using the Caputo operator? What is the main advantages of it on other existing operators with or without singular kernels? 9. The authors are requested to add more details regarding their original contributions in this manuscript. 10. Some figures should be redrawn clearly. 11. Authors should improve the introduction by including the recent development within the frame of COVID-19 pandemic and its variants with the help of recently published papers. I recommend the papers: • Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan. The European Physical Journal Plus, 135(10), 1-42, (2020). • Stability analysis of an incommensurate fractional-order SIR model. Mathematical Modelling and Numerical Simulation with Applications, 1(1), 44-55, (2021). • A new mathematical modeling of the COVID-19 pandemic including the vaccination campaign. Open Journal of Modelling and Simulation, 9(3), 299-321, (2021). • Vaccination effect conjoint to fraction of avoided contacts for a Sars-Cov-2 mathematical model. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 56-66, (2021). • Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay. Computers in Biology and Medicine, 105115, 141, (2022). • Dynamics of cholera disease by using two recent fractional numerical methods. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 102-111, (2021). • Chaos of calcium diffusion in Parkinson’s infectious disease model and treatment mechanism via Hilfer fractional derivative. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 84-94, (2021). • Fractional-order mathematical modelling of cancer cells-cancer stem cells-immune system interaction with chemotherapy. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 67- 83, (2021). 12. What is the novelty of your work? There are some similar papers which investigated in this area, although there are some minor differences in the structure and applications to the COVID-19 models. Please state it clearly. 13. Have you employed any specific assumptions in your COVID-19 model? Please explain briefly. 14. More biological interpretations should be given. Please provide corresponding explanations of the figures in terms of their biological meanings and the pointing out the novelty of the paper. How do figures support your scheme? It will be more helpful to readers to have some discussions about insight of the main results and outcomes of the figures. Briefly, I recommend publishing after doing above MAJOR REVISIONS. So, I want to read speedily the revised version of paper before publishing if it is possible for you. With many thanks and best regards. . . ******* 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No Reviewer #2: No Reviewer #3: No ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. Attachments Attachment Submitted filename: Reviewer Report [PONE-D-22-16861].pdf https://doi.org/10.1371/journal.pone.0278880.r001
Revision 1
16 Oct 2022 Author Response Manuscript ID: PONE-D-22-16861 Reply to the reviewers’ comments on the manuscript entitled “Fractional order SEIQRD epidemic model of Covid-19: a case study of Italy” submitted to the Journal “PLOS ONE”. Reviewer #1: The presentation should be improved. Introduction need attention. Some recent work on COVID-19 relevant to this paper should be cited like: Chaos, Solitons& Fractals 157 (2022): 111955,Results in Physics 19 (2020): 103510.Alexandria Engineering Journal 59.5 (2020): 3221-3231.Results in physics 19 (2020): 103560.Results in Physics (2022): 105649 Authors’ response: Authors have modified the introduction part; some important recent and relevant references along with the one mentioned by the reviewer has been included. Reviewer #2: After reading this paper in detail, this paper needs to be revised via follows: The Abstract should contain answers to the following questions: What problem was studied and why is it important? What methods were used? What are the important results? What conclusions can be drawn from the results? What is the novelty of the work and where does it go beyond previous efforts in the literature? Authors’ response: Authors have modified the abstract as per the reviewer’s suggestions. [12-16] these papers should be written in clearly Authors’ response: We have rewritten the description of these papers [12-16]. "4.3 The Equilibrium Points of the system" this part of the paper needs to be extended a little more. Authors’ response: Authors have modified this section (4.3 The Equilibrium Points of the system). They need to present more information about the novelty of this paper. Authors’ response: Authors have modified the introduction part. The novelty and contribution of the work is clearly explained. What is the main contribution of this paper when we compare it via follows DOI:10.1080/17455030.2022.2075954; Modified Predictor–Corrector Method for the Numerical Solution of a FractionalOrder SIR Model with 2019-nCoV; Symmetry, 13(2428), 1-18, 2021;Chaos, Solitons and Fractals, 158(112050), 1-6, 2022; DOI:10.1142/S1793962323500083? Authors’ response: The authors would like to draw your attention towards the fact that the innovativeness of the paper lies in the consideration of the fractional order derivative of the population compartments. It is observed that fractional order derivatives reflect better results than integral order. Also the authors have modified abstract and introduction part; some important recent and relevant references along with the one mentioned by the reviewer has been included. What is the advantage of this operator used in this paper? Authors’ response: Fractional derivatives are a powerful tool for describing memory and heredity characteristics in a wide range of systems and phenomena. Fractional-order differential equations store the function's comprehensive information in stacked form. Caputo fractional differentiations and differential equations have quite a number of useful advantages. When dealing with real-world problems, the Caputo derivative is particularly useful since it allows traditional initial and boundary conditions and the derivative of a constant is zero, which is not the case with the Riemann–Liouville fractional derivative. For this chapter of the paper "4.2 Non-negativity and boundedness of proposed model", they didnt cite any paper. Thus, they need to cite at least one paper related to this part of the paper. Authors’ response: Authors have added one citation in this part. Reviewer #3: Reviewer Report on: Title: Fractional order SEIQRD epidemic model of Covid-19: a case study of Italy Journal: PLOS ONE Manuscript ID: PONE-D-22-16861 Authors: Mahata et al. Overall Comments: The authors have examined the fractional order SEIQRD compartmental model in a fractional order framework to account for the uncertainty caused by the lack of information regarding the Coronavirus (COVID-19). In addition, the fractional-order Taylor’s approach is utilized to approximate the solution to the proposed model. The model’s validity is demonstrated by comparing real-world data with simulation outcomes. Furthermore, the system’s analysis and numerical findings show that regular usage of face masks can help to reduce the COVID-19 epidemic. However, it needs some revisions from the point of authors and readers to improve the quality of the paper. After these MAJOR REVISIONS, I suggest that this paper can be accepted to publish in ” PLOS ONE”. My comments are as follows: 1. Ensure the end of each line of the equations has a punctuation, either a comma or a full stop if it is the end of the equation - these are missing in several of the equations, see for example: Authors’ response: We are extremely sorry for that. All such errors have been edited and re-edited. 2. The Introduction should make a compelling case for why the study is useful along with a clear statement of its novelty or originality by providing relevant information and providing answers to basic questions such as: • What is already known in the open literature? • What needs to be done, why and how? Authors’ response: The novelty and contribution of the work is clearly explained. The Introduction part of the manuscript contains extensive discussion of previous and related work along with relevant references. The research method adopted in this work are however original. 3. Clear statements of the novelty of the work should also appear briefly in the Abstract and Conclusions sections. Authors’ response: Authors have modified the introduction part. The novelty and contribution of the work is clearly explained. 4. How did they decide the Lyapunov function in the global stability analysis? Authors’ response: An important technique in stability theory for differential equations is known as the direct method of Lyapunov. Let us consider a nonlinear time-invariant system, x' = f(x), where f(x) is assumed to be locally Lipschitz in x. Let xe be the equilibrium point of the system such that f(xe) = 0. The Lyapunov's Direct Method generally says that if you can find a continuous differentiable function V(x) satisfying the following conditions: V(x) > 0 (positive definite) and V(0) = 0, V'(x) = (∂V/∂x)•f(x) ≤ – W(x) ≤ 0, V(x) → ∞ as \|\|x\|\| → ∞. Then the equilibrium point xe is globally stable if W(x) ≥ 0 (positive semi-definite), and globally asymptotically stable if W(x) > 0 (positive definite) for all x ≠ 0. 5. How did they decide determining the initial conditions? Authors’ response: Authors have modified the numerical section. 6. What about the parameter values in the system. Where they have been taken them from? Authors’ response: The references for parameters in Table 2 are reflected clearly in the last column of Table 2 in the numerical section. 7. Why did they ignore the fractional order in the system? Is it dimentionally correct now? Discuss the system by comparing the following literature. • Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom. Chaos, Solitons& Fractals, 111954, (2022). • Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey. Computers in biology and medicine, 105044, (2021). Authors’ response: We admit of a gross mistake in ignoring the parameters instead of redefining them. Necessary corrections have been made. We are extremely thankful to the reviewer for drawing our attention towards the relevant issue. 8. What is the main motivation in using the Caputo operator? What are the main advantages of it on other existing operators with or without singular kernels? Authors’ response: Fractional order modelling is a useful tool that has been used to explore the nature of diseases since the fractional derivative is an extension of the integer-order derivative. In order to replicate real-world issues, several innovative fractional operators with various properties have been designed. In addition, the integer derivative has a local identity, whereas the fractional derivative has a global character. The Caputo derivative is particularly useful for discussing real-world situations since it permits traditional beginning and boundary conditions to be used in the derivation, and the derivative of a constant is zero, whereas the Riemann–Liouville fractional derivative does not. Numerous varieties of fractional derivatives, both with and without singular kernels, are available today. Leibniz's query from 1695 marks the beginning of the fractional derivative. The fractional derivative also improves in the improvement of the system's consistency domain. We have the derivatives of Caputo, Riemann-Liouville, and Katugampola for singular kernels.There are two varieties of fractional derivatives without singular kernels: the Caputo-Fabrizio fractional derivative, which has an exponential kernel, and the Atangana-Baleanu fractional derivative, which has a Mittag-Leffler kernel. 9. The authors are requested to add more details regarding their original contributions in this manuscript. Authors’ response: The Introduction part of the manuscript contains extensive discussion of previous and related work along with relevant references. The research method adopted in this work are however original. 10. Some figures should be redrawn clearly. Authors’ response: Almost all figures have been well explained to get a better clarity regarding the biological aspect. 11. Authors should improve the introduction by including the recent development within the frame of COVID-19 pandemic and its variants with the help of recently published papers. I recommend the papers: • Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan. The European Physical Journal Plus, 135(10), 1-42, (2020). • Stability analysis of an incommensurate fractional-order SIR model. Mathematical Modelling and Numerical Simulation with Applications, 1(1), 44-55, (2021). • A new mathematical modeling of the COVID-19 pandemic including the vaccination campaign. Open Journal of Modelling and Simulation, 9(3), 299-321, (2021). • Vaccination effect conjoint to fraction of avoided contacts for a Sars-Cov-2 mathematical model. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 56-66, (2021). • Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay. Computers in Biology and Medicine, 105115, 141, (2022). • Dynamics of cholera disease by using two recent fractional numerical methods. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 102-111, (2021). • Chaos of calcium diffusion in Parkinson’s infectious disease model and treatment mechanism via Hilfer fractional derivative. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 84-94, (2021). • Fractional-order mathematical modelling of cancer cells-cancer stem cells-immune system interaction with chemotherapy. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 67- 83, (2021). Authors’ response: Authors have modified the introduction part; some important recent and relevant references along with the one mentioned by the reviewer has been included. 12. What is the novelty of your work? There are some similar papers which investigated in this area, although there are some minor differences in the structure and applications to the COVID-19 models. Please state it clearly. Authors’ response: Authors have modified the introduction part. The novelty and contribution of the work is clearly explained. 13. Have you employed any specific assumptions in your COVID-19 model? Please explain briefly. Authors’ response: The Introduction part of the manuscript contains extensive discussion of previous and related work along with relevant references. The research method adopted in this work are however original. 14. More biological interpretations should be given. Please provide corresponding explanations of the figures in terms of their biological meanings and the pointing out the novelty of the paper. How do figures support your scheme? It will be more helpful to readers to have some discussions about insight of the main results and outcomes of the figures. Briefly, I recommend publishing after doing above MAJOR REVISIONS. So, I want to read speedily the revised version of paper before publishing if it is possible for you. Authors’ response: Figures have been well explained to get a better clarity regarding the biological aspect. The authors are thankful to the reviewers and editor for their valuable comments and suggestions which also helped in improving the quality of our work. Attachments Attachment Submitted filename: Reply to reviewers comment_Plos one_August 2022.docx* https://doi.org/10.1371/journal.pone.0278880.r002
28 Nov 2022 Decision Letter - Pablo Martin Rodriguez, Editor Fractional order epidemic model of Covid-19: a case study of Italy PONE-D-22-16861R1 Dear Dr. Mahata, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Pablo Martin Rodriguez Academic Editor PLOS ONE Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation. Reviewer #2: All comments have been addressed Reviewer #3: All comments have been addressed ******** 2. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #2: (No Response) Reviewer #3: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #2: (No Response) Reviewer #3: N/A ****** 4. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #2: (No Response) Reviewer #3: Yes ****** 5. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #2: (No Response) Reviewer #3: Yes ****** 6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #2: (No Response) Reviewer #3: After reading the revised form of the manuscript, I am convinced that the authors have improved their previous version that making it now suitable for acceptance by the PLOS ONE journal. ****** 7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #2: No Reviewer #3: No ******** https://doi.org/10.1371/journal.pone.0278880.r003
Formally Accepted
1 Dec 2022 Acceptance Letter - Pablo Martin Rodriguez, Editor PONE-D-22-16861R1 Fractional order SEIQRD epidemic model of Covid-19: a case study of Italy Dear Dr. Mahata: I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org. If we can help with anything else, please email us at plosone@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Professor Pablo Martin Rodriguez Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0278880.r004

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