A conformable fractional finite difference method for modified mathematical modeling of SAR-CoV-2 (COVID-19) disease

Syeda Alishwa Zanib; Tamour Zubair; Sehrish Ramzan; Muhammad Bilal Riaz; Muhammad Imran Asjad; Taseer Muhammad

doi:10.1371/journal.pone.0307707

Peer Review History

Original SubmissionAugust 8, 2023
13 Nov 2023 Decision Letter - Renier Mendoza, Editor PONE-D-23-25335A Conformable Fractional Finite Difference Method for Modified Mathematical Modeling of SAR-CoV-2 (COVID-19) DiseasePLOS ONE Dear Dr. Zubair, 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. Please submit your revised manuscript by Dec 28 2023 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. 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If you wish to make changes to your Data Availability statement, please describe these changes in your cover letter and we will update your Data Availability statement to reflect the information you provide. 5. Please update your submission to use the PLOS LaTeX template. The template and more information on our requirements for LaTeX submissions can be found at http://journals.plos.org/plosone/s/latex. [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: Partly Reviewer #3: Yes ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: N/A 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: No 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: No 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: In the present manuscript investigate modified and comprehensive mathematical model that captures the complex relationships between various population compartments, including susceptible, infected, exposed, recovered, vaccinated, and quarantined people. Using conformable derivatives, we provide a system of equations that precisely captures the complex interconnections inside the COVID-19 transmission. This field also has a wide applications. Clearly organized in analytical as well as numerical part. The work of the paper is good. However, there are some comments to improve the quality of the paper which are given as follows: [1.] Model formation is unclear, explain it well. [2.] Explain novelty or key contributions of your work in the end of introduction part. [3.] There are lot of grammatical error, some typos and punctuation problems are exist that should be checked and corrected throughout the paper. [4.] What about the solution of system? [5.] What is the main objective of the research presented in the abstract, and why is it important in the context of the COVID-19 pandemic? [6.] How does the mathematical model described in the abstract account for the different population compartments, and what role do conformable derivatives play in this model? [7.] What methods were used for performing calculations in this research, and why was MAPLE-2019 chosen for these calculations? [8.] How you fix the initial values of the model? [9.] In Introduction part, Start with mathematical modeling and add some important works related with recent development in mathematical modeling such as Biomedical Signal Processing and Control, 84, 2023, 104714; Results in Physics, 2023, 106489; Nonlinear Dynamics, 111 4879-4914, 2023; Symmetry, 15(4), 845, 2023; Optimal Control, Applications and Methods, (43)(3), 842-866, 2022; Nonlinear Dynamics, 109 3169{3187, 2022. Reviewer #2: The manuscript presented a mathematical model using conformable fractional derivatives for COVID-19 with quarantine and vaccination. The authors claim that by using conformable derivatives, the resulting system of equations “precisely captures” the complex interconnections in the COVID-19 transmission. While I applaud the authors’ efforts in this regard, the paper does not provide sufficient analysis and/or numerical results to support this claim. I suggest that the authors revisit their work and hire a copyeditor. Some guide questions/suggestions that may help improve their work: - Why use conformable derivatives over other fractional derivatives? What are the advantages? - Are there drawbacks in using conformable derivatives in comparison to other fractional derivatives and ordinary derivatives? - In what sense does the proposed model based on systems of conformal differential equations “precisely captures” the complex interconnections in the COVID-19 transmission compared to models based on ODE systems or other FDE systems? - What is the main contribution of your work? How does it compare to similar works, e.g. the fractal-fractional model for COVID-19, proposed by Malik et al. (https://doi.org/10.1016/j.aej.2022.02.024), where they also incorporated quarantine and vaccination? Moreover, the literature review in the introduction is quite lengthy, but it mainly focuses on COVID-19 and models based on ODE systems. Related literature on fractional derivatives and mathematical models based on systems of fractional differential equations should be reported in the manuscript. The research objectives should be stated in the introduction. Lastly, it is should be noted that this year 2023, the World Health Organization has declared an end to COVID-19 as a global health emergency, and with the overwhelmingly large number of literature on mathematical models for COVID-19, it is crucial that the authors highlight the main contribution of their work in this vast field. Unfortunately, in its current state, I believe the material is too underdeveloped. For these reasons, I cannot recommend accepting this paper for publication. Reviewer #3: Authors have constructed novel results. I recommend but need major concerns like: 1. Check the stability of the method. 2. Why existence uniqueness is considered. For such existence refer original work like:On nonlinear conformable fractional order dynamical system via differential transform method." CMES-Computer Modeling in Engineering & Sciences 136.2 (2023): 1457-1472.Existence and stability theory of pantograph conformable fractional differential problem." Thermal Science 27.Spec. issue 1 (2023): 237-244.Mathematical analysis of fractional order alcoholism model." Alexandria Engineering Journal 78 (2023): 281-291. 3. Discuss the convergence of the numerical method. 4. Why this method is powerful than other refer some work like: The Volterra-Lyapunov matrix theory and nonstandard finite difference scheme to study a dynamical system." Results in Physics 52 (2023): 106890.Study of transmission dynamics of novel COVID-19 by using mathematical model." Advances in Difference Equations 2020 (2020): 1-13.To study the transmission dynamic of SARS-CoV-2 using nonlinear saturated incidence rate." Physica A: Statistical Mechanics and its Applications 604 (2022): 127915. 4.Discuss graphs biologically. 5.Update the conclusion with future work. ****** 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: PONE-D-23-25335.pdf https://doi.org/10.1371/journal.pone.0307707.r001
Revision 1
12 Feb 2024 Author Response Response to reviewer’s comments Manuscript ID: PONE-D-23-25335 Journal Name: PLOS One Dear Associate Editor, Thank you for your useful comments on our manuscript. We have considered your editorial or reviewer's comments and made the following changes to our paper entitled "A Conformable Fractional Finite Difference Method for Modified Mathematical Modeling of SAR-CoV-2 (COVID-19) Disease." We have modified the manuscript accordingly, and detailed corrections are listed below point by point. All the changes are highlighted in red, blue, and green color for Referees 1, 2 and, 3 respectively, in the paper. Comments from Reviewers and Answers Reviewer: I In the present manuscript investigate modified and comprehensive mathematical model that captures the complex relationships between various population compartments, including, susceptible, exposed, recovered, vaccinated, and quarantined people. Using Conformable derivatives, we provide a system of equations that precisely captures the complex interconnections inside the COVID-19 transmission. This field also have a wide application. Clearly organized in analytical as well as numerical part. The work of the paper is good. However, there are some comments to improve the quality of paper which are given as follows: 1. Model formation is unclear, explain it well. Response. The detail model formulation has been added 2. Explain the novelty or key contributions of your work at the end of the introduction part. Response. Query has been fixed 3. There are lot of grammatical errors, some typos and punctuation problems are exist that should be checked and corrected throughout the paper. Response. All grammar errors have been removed accordingly 4. What about the solution of the system? Response. We calculate the solution of the system using the finite difference method. 5. What is the main objective of the research presented in the abstract, and why is the important in the context of the COVID-19 pandemic? Response. The query has been fixed. 6. How does the mathematical model described in the abstract account for the different population compartments, and what role do conformable derivatives play in the model? Response. The mathematical model described in the abstract incorporates different population compartments by utilizing a six-dimensional compartmental model. Conformable derivatives play a crucial role in the model by introducing fractional-order dynamics. 7. What method used for performing calculations in this research, and why was MAPLE-19 chosen for these calculations? Response: FDM is used for calculation. MAPLE-19 was chosen as the tool for these calculations because it's like a super-smart calculator. It's good at working with symbols and equations, which is important when dealing with complex math. 8. How you fix the initial values of model? Response: Initial conditions have been set using literature. 9. In introduction part, start with mathematical modelling and add some important works related with recent development in mathematical modelling such as biomedical signal processing and control, 84, 2023, 104714; Results in Physics, 2023, 106489; Nonlinear Dynamics,111, 4879-4914, 2023; Symmetry, 15(4), 854, 2023; optimal control, Applications and Methods, (43)(3), 842-866, 2022; Nonlinear Dynamics, 109 3169(3187),2022. Response: The introduction has been modified using the suggested reference. Reviewer II The manuscript a mathematical model using conformable fractional derivatives for Covid-19 with quarantine and vaccinations, The authors claim that by using conformable derivatives, the resulting system of equations precisely captures the complex interconnections in COVID-19 transmission. While I applaud the author’s efforts in this regard paper does not provide sufficient analysis and/or numerical results to support this claim. I suggest that the authors revisit their work and hire a copyeditor. Some guide questions/suggestions that may help to improve their work: 1. why use conformable derivatives over other fractional derivatives? What are the advantages? Response: Conformable derivatives play a crucial role in the model by introducing fractional-order dynamics. The beauty of the conformable fractional order derivative is that the solution of the fractional model (9)-(14), tends to the solution of the classical model (1)-(6), as the value of 𝜙 tends to 1. 2. Are there drawbacks in using conformable derivatives in comparison to other fractional derivatives and ordinary derivatives? Response: Conformable derivatives are simpler but may not work in all situations other than fractional and ordinary derivatives. 3. In what sense does the proposed model based on systems of conformal differential equations precisely capture the complex interconnections in the COVID-19, transmission compared to models based on ODE systems or other FDM systems? Response: Applying conformable fractional derivatives to a COVID-19 mathematical model enhances sensitivity to variations, and incorporates memory effects resulting in a more accurate representation of the virus's complex dynamics compared to other models based on ODE systems or FDM systems. 4. What is mean contribution of your work? How does it compare to similar works. e.g the fractal-fractional model for COVID-19 proposed by Malik et al., (https://doi.org/10.1016/j.aej.2022.02.024), where they also incorporated quarantine and vaccinations? Response: We designed the FDM approach of the conformable fractional derivative using the Taylor series and used it on a modified mathematical model of COVID-19 which is the main contribution of the work. 5. Moreover the literature review in the introduction is quite lengthy, but it mainly focuses on COVID-19 and model based on ODE systems. Related literature on fractional derivatives and mathematical models based on systems of fractional differential equations should be represented in the manuscript. The research objectives should be stated in the introduction. Response: The literature review has been updated as suggested. 6. Lastly, it is should be noted that this year 2023, the world health organization has declared an end to COVID-19 as a global health emergency and with overwhelmingly large number of literature on mathematical models for COVID-19, it is crucial that the authors highlights the main contribution of their work in the vast field. Unfortunately, in the current state, I believe that the material is too underdeveloped. For this reason, I cannot recommend accepting this paper for publication. Response: As mentioned already the main focus of the work is the FDM approach of the conformable fractional derivative using the Taylor series and used on a modified mathematical model of COVID-19 Reviewer III Authors have constructed novel results. I recommend but need major concerns like: 1. Check the stability of the method. Response: We check the stability of the model at a disease-free equilibrium point. In the numerical section, we also check the stability analysis of the numerical scheme 2. Why existences uniqueness is considered. For such existence refer original work like : on nonlinear conformable fractional order dynamical system via differential transform method. CMES.Computer Modeling in Engerning & science 136.2 (2023): 1457-1472. Existence and stability theory of pantograph conformable fractional differential problem. Thermal Science 27.spec. issue 1 (2023): 237-244. Mathematical analysis of fractional order alcoholism model. Alexandria Engerning journal 78 (2023): 281-291. Response: Existence and uniqueness considerations in mathematical models ensure that solutions are well-defined and meaningful. For the method, suitable reference has been cited. 3. Discus the convergence of the numerical method. Response: Convergence of numerical scheme has been discussed. 4. Why this method is powerful than other refer work like. The Volterra-Lyapunov matrix theory and non-understand finite difference scheme to study a dynamical system. Results in Physics 52 (2023): 106890. Study a transmission dynamical of novel COVID-19 by using a mathematical model. Advanced in differential equations 2020(2020): 1-13. To study the transmission dynamics of SARS-COV-2 using a nonlinear saturated incidence rate. Physics A: Statistical Mechanics and its Applications 604 (2022): 127915: Response: The conformable fractional derivative method is better than other methods because it can understand and represent more complex behaviors in systems, making it a more flexible and accurate tool for studying dynamic systems compared to the Volterra-Lyapunov matrix theory. 5. Discuss graphs biologically. Response: Biological Behavior of graphs have been discussed. 6. Update the conclusion with future fork Response: Future directions have been added in conclusion Response to Associate Editor: The authors would like to thank the referees for suggesting specific changes in the original manuscript, for their valuable comments which improved the paper and for their high interest in this work. The manuscript has been resubmitted to your journal. We look forward to your positive response. With Regards, Tamour Zubair https://doi.org/10.1371/journal.pone.0307707.r002
20 Mar 2024 Decision Letter - Renier Mendoza, Editor PONE-D-23-25335R1A Conformable Fractional Finite Difference Method for Modified Mathematical Modeling of SAR-CoV-2 (COVID-19) DiseasePLOS ONE Dear Dr. Zubair, 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. Please refer to the comments and suggestions below as you revise the manuscript. Please submit your revised manuscript by May 04 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols. We look forward to receiving your revised manuscript. Kind regards, Renier Mendoza Academic Editor PLOS ONE Journal Requirements: Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. Additional Editor Comments: During the initial revision of the manuscript, THREE additional authors were included. In your response letter, please specify the sections of the manuscript to which each author contributed and explain the significance of their contributions. Additionally, please explain why the original authors are unable to revise the manuscript independently without the assistance of the new authors. Failure to provide justification for the inclusion of these authors may lead to rejection. [Note: HTML markup is below. Please do not edit.] 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 #1: (No Response) Reviewer #2: All comments have been addressed Reviewer #3: (No Response) ******** 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 #1: Yes Reviewer #2: Partly Reviewer #3: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: N/A Reviewer #3: Yes ****** 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 #1: Yes Reviewer #2: Yes 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 #1: Yes Reviewer #2: No Reviewer #3: No ****** 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 #1: The authors' revisions have been duly noted. Consequently, I hereby accept the manuscript. Their diligent updates have enhanced its quality, addressing concerns and refining content. Their efforts reflect a commitment to scholarly excellence, ensuring the work meets publication standards. Acknowledging their dedication, I endorse the manuscript for inclusion. This decision underscores its significance and contribution to the field. I anticipate its impact on readers and its role in advancing knowledge. With confidence in its merit, I affirm my acceptance of the manuscript, appreciating the authors' contributions and the collective endeavor towards academic advancement. Reviewer #2: The authors were able to address some comments in the first revision. In my opinion, the paper can be accepted after revision taking into consideration the following points. 1. An in-depth discussion in the paper is necessary to establish why the proposed model based on conformable fractional derivative is better than classical models based on ODE systems. These needs to be highlighted as well in the numerical results. 2. The paper claims that the use of a finite difference approach over classical numerical methods gives "high convergence", but the paper fails to satisfatorily establish this, both theoretically and numerically. 3. There are still grammatical, typographical, punctuation, and typesetting issues. I urge the authors to hire a copyeditor to help address these issues. Reviewer #3: Authors have not addressed all my comments. Graphical illustrations need explanations. Typos exist there. Still the literature need to update about the NSFD method. It is strongly recommend to put relevant references about the methodology been used for COVID-19. Authors have ignored these . They must cite the research work relevant to COVID-19 recently available like: Study of a mathematical model of COVID-19 outbreak using some advanced analysis." Waves in Random and Complex Media (2022): 1-18.Study of integer and fractional order COVID-19 mathematical model." Fractals (2023): 2340046.Fractional order modeling of predicting covid-19 with isolation and vaccination strategies in morocco." CMES-Comput. Model. Eng. Sci 136 (2023): 1931-1950.On a SEIR-type model of COVID-19 using piecewise and stochastic differential operators undertaking management strategies." (2023). For NSFD cite these work: Results in Physics 52 (2023): 106890, Results in Physics 24 (2021): 104069. Update the literature about applications of mathy. models like: Statistical and computational analysis for corruption and poverty model using Caputo-type fractional differential equations." Heliyon (2024)., A Fractal-Fractional Order Model to Study Multiple Sclerosis: A Chronic Disease." Fractals (2024): 2440010. South African Journal of Chemical Engineering 48 (2024): 63-70. ****** 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 #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. https://doi.org/10.1371/journal.pone.0307707.r003
Revision 2
2 May 2024 Author Response Response to reviewer’s comments Manuscript ID: PONE-D-23-25335 Journal Name: PLOS One Dear Associate Editor, Thank you for your useful comments on our manuscript. We have considered your editorial or reviewer's comments and made the following changes to our paper entitled " A Conformable Fractional Finite Difference Method for Modified Mathematical Modeling of SAR-CoV-2 (COVID-19) Disease". We have modified the manuscript accordingly, and detailed corrections are listed below point by point. All the changes are highlighted in green, blue, and red color for Referee 1, Referee 2, and Referee 3, respectively in the paper. Comments from Reviewers and Answers Reviewer: I The authors' revisions have been duly noted. Consequently, I hereby accept the manuscript. Their diligent updates have enhanced its quality, addressing concerns and refining content. Their efforts reflect a commitment to scholarly excellence, ensuring the work meets publication standards. Acknowledging their dedication, I endorse the manuscript for inclusion. This decision underscores its significance and contribution to the field. I anticipate its impact on readers and its role in advancing knowledge. With confidence in its merit, I affirm my acceptance of the manuscript, appreciating the authors' contributions and the collective endeavor toward academic advancement. Response: We're grateful to you for your positive feedback and acceptance of our revised manuscript. Reviewer: II The authors were able to address some comments in the first revision. In my opinion, the paper can be accepted after revision taking into consideration the following points. 1. An in-depth discussion in the paper is necessary to establish why the proposed model based on conformable fractional derivative is better than classical models based on ODE systems. These need to be highlighted as well in the numerical results. Response: We appreciate the reviewer's suggestion and agree that an in-depth discussion is crucial. In our revised manuscript, we will elaborate conformable fractional derivative is better than classical models based on ODE systems. We will also enhance our numerical results section to include a comparative analysis demonstrating how our fractional derivative model provides improved accuracy and insight into system behaviours as the fractional parameter ϕ approaches 1, thereby bridging the understanding between classical and fractional models in the discussion section. 2. The paper claims that the use of a finite difference approach over classical numerical methods gives "high convergence", but the paper fails to satisfactorily establish this, both theoretically and numerically. Response: Table 3 explains that the finite difference approach gives high convergence results. 3. There are still grammatical, typographical, punctuation, and typesetting issues. I urge the authors to hire a copyeditor to help address these issues. Response: All grammatical, typographical, punctuation, and typesetting issues have been removed. Reviewer: III The authors have not addressed all my comments. 1. Graphical illustrations need explanations. Typos exist there. Response: Thank you for your kind suggestion. Graphical explanations have been added and remove all typos. 2. Still, the literature needs to be updated about the NSFD method. It is strongly recommended to put relevant references about the methodology used for COVID-19. Authors have ignored these. They must cite the research work relevant to COVID-19 recently available like: Study of a mathematical model of COVID-19 outbreak using some advanced analysis." Waves in Random and Complex Media (2022): 1-18. Study of integer and fractional order COVID-19 mathematical model." Fractals (2023): 2340046.Fractional order modeling of predicting covid-19 with isolation and vaccination strategies in Morocco." CMES-Comput. Model. Eng. Sci 136 (2023): 1931-1950.On an SEIR-type model of COVID-19 using piecewise and stochastic differential operators undertaking management strategies." (2023). For NSFD cite these work: Results in Physics 52 (2023): 106890, Results in Physics 24 (2021): 104069. Update the literature about applications of mathy. models like: Statistical and computational analysis for corruption and poverty model using Caputo-type fractional differential equations." Heliyon (2024)., A Fractal-Fractional Order Model to Study Multiple Sclerosis: A Chronic Disease." Fractals (2024): 2440010. South African Journal of Chemical Engineering 48 (2024): 63-70. Response: All suitable references have been cited according to instructions. Response to Associate Editor: The authors would like to thank the referees for suggesting specific changes in the original manuscript, for their valuable comments which improved the paper and for their high interest in this work. The manuscript has been resubmitted to your journal. We look forward to your positive response. With Regards, Tamour Zubair Attachments Attachment Submitted filename: Response Letter plos 2nd.pdf https://doi.org/10.1371/journal.pone.0307707.r004
7 May 2024 Decision Letter - Renier Mendoza, Editor PONE-D-23-25335R2A Conformable Fractional Finite Difference Method for Modified Mathematical Modeling of SAR-CoV-2 (COVID-19) Disease PLOS ONE Dear Dr. Zubair, 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. Specifically, the authors did not address a very important point. During the initial revision of the manuscript, THREE additional authors were added. I am sending the manuscript back to the authors before sending it again for review. Please revise your response letter and specify the sections of the manuscript to which each author contributed and explain the significance of their contributions. Additionally, please explain why the original authors are unable to revise the manuscript independently without the assistance of the new authors. Failure to provide justification for the inclusion of these authors during the revision may lead to rejection. PLOS is a member of the Committee on Publication Ethics (COPE). PLOS ONE abides by its Code of Conduct and aims to adhere to its Best Practice Guidelines. Authors are expected to comply with best practices in publication ethics, specifically concerning authorship, dual publication, plagiarism, figure manipulation, and competing interests. Please submit your revised manuscript by Jun 21 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. 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Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. [Note: HTML markup is below. Please do not edit.] [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. https://doi.org/10.1371/journal.pone.0307707.r005
Revision 3
27 May 2024 Author Response Response to reviewer’s comments Manuscript ID: PONE-D-23-25335 Journal Name: PLOS One Dear Associate Editor, Thank you for your useful comments on our manuscript. We have considered your editorial or reviewer's comments and made the following changes to our paper entitled " A Conformable Fractional Finite Difference Method for Modified Mathematical Modeling of SAR-CoV-2 (COVID-19) Disease". We have modified the manuscript accordingly, and detailed corrections are listed below point by point. All the changes are highlighted in green, blue, and red color for Referee 1, Referee 2, and Referee 3, respectively in the paper. Comments from Reviewers and Answers Reviewer: I The authors' revisions have been duly noted. Consequently, I hereby accept the manuscript. Their diligent updates have enhanced its quality, addressing concerns and refining content. Their efforts reflect a commitment to scholarly excellence, ensuring the work meets publication standards. Acknowledging their dedication, I endorse the manuscript for inclusion. This decision underscores its significance and contribution to the field. I anticipate its impact on readers and its role in advancing knowledge. With confidence in its merit, I affirm my acceptance of the manuscript, appreciating the authors' contributions and the collective endeavor toward academic advancement. Response: We're grateful to you for your positive feedback and acceptance of our revised manuscript. Reviewer: II The authors were able to address some comments in the first revision. In my opinion, the paper can be accepted after revision taking into consideration the following points. 1. An in-depth discussion in the paper is necessary to establish why the proposed model based on conformable fractional derivative is better than classical models based on ODE systems. These need to be highlighted as well in the numerical results. Response: We appreciate the reviewer's suggestion and agree that an in-depth discussion is crucial. In our revised manuscript, we will elaborate conformable fractional derivative is better than classical models based on ODE systems. We will also enhance our numerical results section 4 to include a comparative analysis demonstrating how our fractional derivative model provides improved accuracy and insight into system behaviours as the fractional parameter 𝜙 approaches 1, thereby bridging the understanding between classical and fractional models in the discussion section. 2. The paper claims that the use of a finite difference approach over classical numerical methods gives "high convergence", but the paper fails to satisfactorily establish this, both theoretically and numerically. Response: Table 3 explains that the finite difference approach gives high convergence results. 3. There are still grammatical, typographical, punctuation, and typesetting issues. I urge the authors to hire a copyeditor to help address these issues. Response: All grammatical, typographical, punctuation, and typesetting issues have been removed. Reviewer: III The authors have not addressed all my comments. 1. Graphical illustrations need explanations. Typos exist there. Response: Thank you for your kind suggestion. Graphical explanations have been added and remove all typos. 2. Still, the literature needs to be updated about the NSFD method. It is strongly recommended to put relevant references about the methodology used for COVID-19. Authors have ignored these. They must cite the research work relevant to COVID-19 recently available like: Study of a mathematical model of COVID-19 outbreak using some advanced analysis." Waves in Random and Complex Media (2022): 1-18. Study of integer and fractional order COVID-19 mathematical model." Fractals (2023): 2340046.Fractional order modeling of predicting covid-19 with isolation and vaccination strategies in Morocco." CMES-Comput. Model. Eng. Sci 136 (2023): 1931- 1950.On an SEIR-type model of COVID-19 using piecewise and stochastic differential operators undertaking management strategies." (2023). For NSFD cite these work: Results in Physics 52 (2023): 106890, Results in Physics 24 (2021): 104069. Update the literature about applications of mathy. models like: Statistical and computational analysis for corruption and poverty model using Caputo-type fractional differential equations." Heliyon (2024)., A Fractal-Fractional Order Model to Study Multiple Sclerosis: A Chronic Disease." Fractals (2024): 2440010. South African Journal of Chemical Engineering 48 (2024): 63-70. Response: Thank you for your suggestions. All suitable references have been cited according to instructions. Response to Associate Editor: The authors would like to thank the referees for suggesting specific changes in the original manuscript, for their valuable comments which improved the paper and for their high interest in this work. The manuscript has been resubmitted to your journal. We look forward to your positive response. With Regards, Tamour Zubair Response Letter Respected Editor, We appreciate your feedback and the opportunity to revise our manuscript. We have thoroughly considered your comments regarding the inclusion of additional authors and would like to provide the necessary clarifications and justifications: Contributions of the Original Authors: • Syeda Alishwa Zanib: Originated the manuscript's main idea. Responsibilities included writing the original draft, review and editing, methodology development, and conceptualization. • Tamour Zubair: Contributed to review and editing, methodology enhancement, and software development. • Sehrish Ramzan: Focused on methodology development, software support, and manuscript review. Contributions of the Additional Authors: • Muhammad Bilal Riaz: Contributed to the graphical Analysis. Muhammad Bilal Riaz provided significant expertise in advanced statistical and numerical methods, which were crucial for the thorough analysis presented in Section 3.3 and 4 of the manuscript. Their contribution has enhanced the reliability of the results. • Muhammad Imran Asjad: Played a pivotal role in the statistical and numerical analysis of design fractional method. Muhammad Imran Asjad 's expertise in fieldwork and fractional methodologies was indispensable for the accuracy and comprehensiveness of the data presented in Section 4.5. Their involvement ensured that the design method adhered to the highest standards of scientific rigor. • Taseer Muhammad: Assisted in the revision of the discussion and conclusion sections. Taseer Muhammad brought a fresh perspective and contributed to a more in-depth interpretation of the results, particularly in Sections 4.1 and 5. Their insights helped to contextualize the findings within the broader scope of existing literature and proofread. The decision to include these additional authors was based on their substantial contributions to key sections of the manuscript, which were beyond the expertise of the original authors. The revisions required a multidisciplinary approach to ensure the manuscript's quality and integrity, and the added expertise of Muhammad Bilal Riaz, Muhammad Imran Asjad, and Taseer Muhammad was essential to meet these high standards. The original authors recognized that the complexity of the revisions necessitated specialized knowledge and skills that the new authors possess. Their collaboration has been instrumental in addressing the reviewers' comments comprehensively and improving the overall quality of the manuscript. We assure you that the inclusion of these authors is in full compliance with the best practices in publication ethics, as they have each made significant and direct contributions to the work. We believe that their involvement is fully justified and that their expertise has greatly enhanced the manuscript. Thank you for your consideration. Sincerely, Tamour Zubair Attachments Attachment Submitted filename: Response Letter plos 2nd.pdf https://doi.org/10.1371/journal.pone.0307707.r006
4 Jun 2024 Decision Letter - Renier Mendoza, Editor PONE-D-23-25335R3A Conformable Fractional Finite Difference Method for Modified Mathematical Modeling of SAR-CoV-2 (COVID-19) DiseasePLOS ONE Dear Dr. Zubair, 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. Kindly refer to the comments below. Please submit your revised manuscript by Jul 19 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols. We look forward to receiving your revised manuscript. Kind regards, Renier Mendoza Academic Editor PLOS ONE Additional Editor Comments: In your response, you mentioned that Muhammad Bilal Riaz provided significant expertise in advanced statistical and numerical methods, which were crucial for the thorough analysis presented in Section 3.3. However, Section 3.3 details the computation of the DFEP, and the computed equilibrium did not change after Riaz joined as an author. You also mentioned that Taseer Muhammad contributed to a more in-depth interpretation of the results in Section 4.1. However, upon closer inspection, theorem 4.1 and its proof did not change after Muhammad joined as an author. The justification for the addition of these authors is not satisfactory. Based on your response, the new authors' contributions are not sufficient for their inclusion in the manuscript. Please revise your response or reconsider adding the new authors. [Note: HTML markup is below. Please do not edit.] [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. https://doi.org/10.1371/journal.pone.0307707.r007
Revision 4
15 Jun 2024 Author Response There was no query from the referees. That is why no response letter to the referees are attached this time. Response to the editor letter is attached to the file to clarify the editor concerns. https://doi.org/10.1371/journal.pone.0307707.r008
10 Jul 2024 Decision Letter - Renier Mendoza, Editor A Conformable Fractional Finite Difference Method for Modified Mathematical Modeling of SAR-CoV-2 (COVID-19) Disease PONE-D-23-25335R4 Dear Dr. Zubair, 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 will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. If you have any questions relating to publication charges, 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, Renier Mendoza Academic Editor PLOS ONE Additional Editor Comments (optional): 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 #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 #3: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #3: Yes ****** 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 #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 #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 #3: Acceptable in current form.Acceptable in current form.Acceptable in current form.Acceptable in current form.Acceptable in current form.Acceptable in current form.Acceptable in current form.Acceptable in current form.Acceptable in current form. ****** 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 #3: No ******** https://doi.org/10.1371/journal.pone.0307707.r009
Formally Accepted
27 Aug 2024 Acceptance Letter - Renier Mendoza, Editor PONE-D-23-25335R4 PLOS ONE Dear Dr. Zubair, I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now being handed over to our production team. At this stage, our production department will prepare your paper for publication. This includes ensuring the following: * All references, tables, and figures are properly cited * All relevant supporting information is included in the manuscript submission, * There are no issues that prevent the paper from being properly typeset If revisions are needed, the production department will contact you directly to resolve them. If no revisions are needed, you will receive an email when the publication date has been set. At this time, we do not offer pre-publication proofs to authors during production of the accepted work. Please keep in mind that we are working through a large volume of accepted articles, so please give us a few weeks to review your paper and let you know the next and final steps. Lastly, 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 customercare@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 Dr. Renier Mendoza Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0307707.r010

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