Smoking and alcoholism dual addiction dissemination model analysis with optimal control theory and cost-effectiveness

Shewafera Wondimagegnhu Teklu; Belela Samuel Kotola; Haileyesus Tessema Alemneh

doi:10.1371/journal.pone.0309356

Peer Review History

Original SubmissionJune 7, 2024
4 Jul 2024 Decision Letter - Joshua Kiddy K. Asamoah, Editor PONE-D-24-23154Modeling and Analysis of Smoking and Alcoholism Dual Addiction Dynamics with Optimal Control Theory and Cost-EffectivenessPLOS ONE Dear Dr. Teklu, 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 Aug 18 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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Please confirm at this time whether or not your submission contains all raw data required to replicate the results of your study. Authors must share the “minimal data set” for their submission. PLOS defines the minimal data set to consist of the data required to replicate all study findings reported in the article, as well as related metadata and methods (https://journals.plos.org/plosone/s/data-availability#loc-minimal-data-set-definition). For example, authors should submit the following data: - The values behind the means, standard deviations and other measures reported; - The values used to build graphs; - The points extracted from images for analysis. Authors do not need to submit their entire data set if only a portion of the data was used in the reported study. If your submission does not contain these data, please either upload them as Supporting Information files or deposit them to a stable, public repository and provide us with the relevant URLs, DOIs, or accession numbers. 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Explain the terms in the basic reproduction number obtained, as done on page 6 of this paper https://doi.org/10.1016/j.heliyon.2023.e20531 after equation (5). Also, comment on the above paper since it is relevant to the current study. 3. What informed the authors' choice of the control terms since the authors did not perform a sensitivity analysis of the parameters in the R0. [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 ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: N/A ****** 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 ****** 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: No Reviewer #2: 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 study seeks to formulate a mathematical model to help mitigate the societal addictions to both smoking and alcohol intake. I find the work interesting if improved. These are my comments to the authors. 1. The abstract of the study contains language construction errors. Also, the statement ". Finally, from the cost-effectiveness analyses we observed that implementing strategy is the most cost-effective strategy." in the abstract is not clear. 2. Authors should desist from citations of the form [24-32] where many papers are cited without explicitly explaining each of them and their results. There are several of them, kindly cite relevant articles with their key results well explained. 3. There are several grammatical errors in the work. Kindly read through the entire paper and correct them. 4. Please reconsider this statement "In the best of our understanding organized from a thorough literature review, no one is studied the smoking and alcoholism dual addiction dissemination in the community using mathematical modeling approach. " From my little search i came across this paper "Bhunu, C. P., & Mushayabasa, S. (2012). A theoretical analysis of smoking and alcoholism. Journal of Mathematical Modelling and Algorithms, 11, 387-408." which has extensively studied alcohol and smoking dual usage. 5. Please change these phrases in the work "minimize and tackle". 6. Read the paper I have given out in point 4 and rewrite your contribution to literature. The novelty of the research is in doubt. Please clarify that. Why is the study not employing fractional calculus but integer order derivatives? 7. The section 2.1 to 2.3 headings are unnecessary. Let them all fall under section 2. 8. Under model formulation, the compartment named as protection definition is ambiguous. Kindly explain that well and further established that from literature. 9. Under model formulation, what do the authors want to communicate regarding the two compartments; addicted and permanently addicted? Please be clear with their definitions and support them with literature. 10. Kindly subject your assumptions to literature. 11. Under schematic diagram, why should a permanently addicted individual (to alcohol or smoking) become a dual addicted before becoming a permanently dual addicted to both? 12. the model failed to consider an alcohol related or smoking related or even alcohol-smoking related death rates. Why? 13. Authors should be explicit as in what it means that their model is positive and bounded. 14. Under the optimal control, authors should be specific with the efforts they are referring to. the controls look abstract in their current form. 15. Why is this "Characterization of Optimal Control" underlined? The paper has formatting problems. Kindly fix that. 16. A number of the model parameters are assumed. Will the model be able to stand the test of time? 17. The conclusion is too long. Paragraph one seems to be overelaborated. Other paragraphs should be simplified. Is there any literature support to your conclusions? Reviewer #2: Review report on the manuscript “Modeling and Analysis of Smoking and Alcoholism Dual Addiction Dynamics with Optimal Control Theory and Cost-Effectiveness” I have carefully read the paper, and it seems interesting. Therefore, the manuscript can be considered further for publication in PLOS ONE if the authors are willing to incorporate a MAJOR Revision. Here under are my specific comments on the manuscript: 1. It is strongly advised and it is the responsibility of the authors to check the whole manuscript and correct all the grammatical errors and typos. The manuscript is full of grammatical errors and typos. It is enough to recommend rejection if the authors fail to thoroughly proofread their revised manuscript. 2. In the abstract, it is not clear on what control interventions were the optimal strategies and cost-effectiveness analysis carried on. 3. The last sentence in the abstract should be split into simple sentences with clear information. 4. There are a number of compound sentences with no clear meanings throughout the manuscript. For instance, see the first sentence under the introduction section. I suggest that the authors split this kind of sentences into simple ones with clear meanings. 5. There are a number of long sentences in the paper. For instance, the first sentence in the first paragraph on the second page is too long. The sentence should be split into simple and meaningful sentences. 6. The literature review should be updated with the following related works: a) https://doi.org/10.1007/s40314-022-01760-2 b) https://www.lhscientificpublishing.com/Journals/articles/DOI-10.5890-JAND.2023.03.004.aspx 7. Description of the parameters delta_1, delta_2, delta_3, rho_1, rho_2 and rho_3 being "modification parameters" as mentioned by the authors in Table 1 is not clear. The physical meanings of the parameters should be given. 8. theta_1 and theta_2 should be described better than just being modification parameters. Please, see the recommended articles in (6) for similar parameter descriptions. 9. In the flowchart in Figure 1, the rate of progression from P_S to C_SA is missing. The authors should fix this. 10. The adjoint variables f_i,i=1,2,...,11 in Equation (21) and thereafter are different from their original definitions (with boldface). The authors should make corrections accordingly. 11. What is the meaning of (.) as appeared in the optimal state variables S, P and others in Theorem 9? 12. Remove the full stop (.) from the caption of all the figures. 13. Revise the captions of Figures 5 to 8 to reflect the specific strategy in terms of Strategy A to Strategy I. ****** 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 ******** [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: Review_report.pdf https://doi.org/10.1371/journal.pone.0309356.r001
Revision 1
16 Jul 2024 Author Response Dear Editor, we have revised our manuscript “Smoking and Alcoholism Dual Addiction Dissemination Model Analysis with Optimal Control Theory and Cost-Effectiveness” accordingly. Editor Comments and Authors Responses Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne-formatting sample main body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne-formatting sample title authors affiliations.pdf Response: We have revised according to our previous experience in PLOS ONE Journal. Please note that PLOS ONE has specific guidelines on code sharing for submissions in which author-generated code underpins the findings in the manuscript. In these cases, we expect all author-generated code to be made available without restrictions upon publication of the work. Please review our guidelines at https://journals.plos.org/plosone/s/materials-and-software-sharing#loc-sharing-code and ensure that your code is shared in a way that follows best practice and facilitates reproducibility and reuse. Response: We agree with this comment We note that your Data Availability Statement is currently as follows: All relevant data are within the manuscript and its Supporting Information files. Response: Since we collected parameter values from published literatures and assumed values for illustration purposes, we mentioned “All relevant data are within the manuscript and its Supporting Information files” in the revised manuscript. Please confirm at this time whether or not your submission contains all raw data required to replicate the results of your study. Authors must share the “minimal data set” for their submission. PLOS defines the minimal data set to consist of the data required to replicate all study findings reported in the article, as well as related metadata and methods (https://journals.plos.org/plosone/s/data-availability#loc-minimal-data-set-definition). For example, authors should submit the following data: - The values behind the means, standard deviations and other measures reported; - The values used to build graphs; - The points extracted from images for analysis. Authors do not need to submit their entire data set if only a portion of the data was used in the reported study. If your submission does not contain these data, please either upload them as Supporting Information files or deposit them to a stable, public repository and provide us with the relevant URLs, DOIs, or accession numbers. For a list of recommended repositories, please see https://journals.plos.org/plosone/s/recommended-repositories. If there are ethical or legal restrictions on sharing a de-identified data set, please explain them in detail (e.g., data contain potentially sensitive information, data are owned by a third-party organization, etc.) and who has imposed them (e.g., an ethics committee). Please also provide contact information for a data access committee, ethics committee, or other institutional body to which data requests may be sent. If data are owned by a third party, please indicate how others may request data access. Response: All relevant data are within the manuscript and its Supporting Information files. Additional Editor Comments: 1. The equation after the statement "The sum of all the differential equations described in equation (4)" should be on a new line and numbered. Response: We have corrected accordingly. 2. Revise the abstract to contain the public health implications of the studies. Response: Since both smoking and alcohol addictions are related to health issues implementing the Strategy A has a great health implication regarding to reduce the dual addiction dissemination problem in the community. Accordingly we have revised the abstract. 3. Explain the terms in the basic reproduction number obtained, as done on page 6 of this paper https://doi.org/10.1016/j.heliyon.2023.e20531 after equation (5). Also, comment on the above paper since it is relevant to the current study. Response: We strongly agree with this strong comment and revised our manuscript accordingly by cited this up-to-date and related paper. See the last part of the sub-section 3.3.2. 4. What informed the authors' choice of the control terms since the authors did not perform a sensitivity analysis of the parameters in the R0. Response: In analysis of our initial manuscript we performed sensitivity analysis but the total number of pages for the manuscript was more than 46 pages due to that we did not incorporated sensitivity analysis. Now since the editor comment 4 is very crucial in the revised manuscript based on the model parameters we have performed the sensitivity analysis together with its associated diagram and justified the corresponding optimal control problem. Reviewer #1: The study seeks to formulate a mathematical model to help mitigate the societal addictions to both smoking and alcohol intake. I find the work interesting if improved. These are my comments to the authors. 1. The abstract of the study contains language construction errors. Also, the statement ". Finally, from the cost-effectiveness analyses we observed that implementing strategy is the most cost-effective strategy." in the abstract is not clear. Response: We revised the abstract accordingly. 2. Authors should desist from citations of the form [24-32] where many papers are cited without explicitly explaining each of them and their results. There are several of them, kindly cite relevant articles with their key results well explained. Response: We have restructured the literatures accordingly. 3. There are several grammatical errors in the work. Kindly read through the entire paper and correct them. Response: We agree with this basic comment and we revised the full manuscript accordingly. 4. Please reconsider this statement "In the best of our understanding organized from a thorough literature review, no one is studied the smoking and alcoholism dual addiction dissemination in the community using mathematical modeling approach.” From my little search i came across this paper "Bhunu, C. P., & Mushayabasa, S. (2012). A theoretical analysis of smoking and alcoholism. Journal of Mathematical Modelling and Algorithms, 11, 387-408, which has extensively studied alcohol and smoking dual usage. Response: We appreciate the reviewer search for similar studies what we have not addressed initially, however, after considering the reviewer comment we totally agree with the comment and searched to get similar studies in the same area thorough literature review and we could not find a study that have been constructed and analyzed the smoking and alcoholism dual addiction dynamics in the community with optimal control strategies and cost-effectiveness. Therefore, our study is different from the study suggested by the reviewer in different aspects. 5. Please change these phrases in the work "minimize and tackle". Response: We have corrected accordingly. 6. Read the paper I have given out in point 4 and rewrite your contribution to literature. The novelty of the research is in doubt. Please clarify that. Why is the study not employing fractional calculus but integer order derivatives? Response: We strongly agree and we have re-written the contribution and novelty of our study by comparing it with other similar studies like mentioned in comment 4. In our study we constructed the integer order model and in the near future any researcher can modify our study by considering fractional order approach to verify the effect of memory. 7. The section 2.1 to 2.3 headings are unnecessary. Let them all fall under section 2. Response: We have ignore all the mentioned section headings accordingly. 8. Under model formulation, the compartment named as protection definition is ambiguous. Kindly explain that well and further established that from literature. Response: The compartment P(t) contains individuals who are protected against either smoking addiction (by education) or alcohol addiction (by education) or dual addiction denoted by P(t). In similar approaches used in the studies of real world situations stated in [30, 31, 32] we considered education as the prevention mechanism. 9. Under model formulation, what do the authors want to communicate regarding the two compartments; addicted and permanently addicted? Please be clear with their definitions and support them with literature. Response: We considered individuals who are addicted with smoking, but, can be improved (rehabilitated by taking treatment) denoted by〖 I〗_S (t), individuals who are permanently addicted with smoking throughout their life (i.e., could not be rehabilitated by taking any treatment measures) denoted by 〖 P〗_S (t), individuals who are addicted with alcohol, but, can be improved (rehabilitated by taking treatment) denoted by〖 I〗_A (t), individuals who are permanently addicted with alcohol throughout their life (i.e., could not be rehabilitated by taking any treatment measures) denoted by 〖 P〗_A (t). Since anxiety against mathematics is a serious social problem we refer for the case of permanent addiction from permanent anxiety from literature [29]. 10. Kindly subject your assumptions to literature. Response: Based on real world problem studies the studies stated in literatures [30, 31, 32] we have revised our model descriptions and assumptions accordingly. 11. Under schematic diagram, why should a permanently addicted individual (to alcohol or smoking) become a dual addicted before becoming a permanently dual addicted to both? Response: We agree with this comment since both options are possible. In our model descriptions and assumptions we considered that individuals in the compartment 〖 C〗_SA are dually addicted but they may be either smoking or alcohol permanent addicted. But, individuals in the compartment 〖 P〗_SA are all permanently dual addicted with both smoking and alcohol. Thus, even though, there is a possibility where a permanently addicted individual (to alcohol or smoking) become a permanently dual addicted to both for the sake of simplicity we assumed that individuals who are either smoking or alcohol permanently addicted will be dually addicted before permanently dually addicted. 12. the model failed to consider an alcohol related or smoking related or even alcohol-smoking related death rates. Why? Response: Initially we ignore death rate with addictions, however, after considering the reviewer comments we incorporated death rates due to illness related with addictions. Therefore, the revised manuscript considers different death rates due to illnesses related with addictions. 13. Authors should be explicit as in what it means that their model is positive and bounded. Response: The model (4) solutions are both positive and bounded in the region Ω={█((S,P,〖 E〗_S,〖 I〗_S,〖 P〗_S,〖 E〗_A,〖 I〗_A,P_A,C_SA,P_SA,T)∈R_+^11,N(t)≤Κ/μ)} means it is invariant and attracting for dual addiction dynamical system (4). Thus, the dual addiction model is mathematically and epidemiologically well-posed and it is sufficient to consider the dynamics of the flow generated by the system (4) in Ω [28, 43]. 14. Under the optimal control, authors should be specific with the efforts they are referring to. the controls look abstract in their current form. Response: We have considered specific control measures such as education, punishment and psychological treatments. 15. Why is this "Characterization of Optimal Control" underlined? The paper has formatting problems. Kindly fix that. Response: We have addressed this comment accordingly. 16. A number of the model parameters are assumed. Will the model be able to stand the test of time? Response: In this study, to perform sensitivity analysis and to simulate the optimal control problem we adopted most of the parameter values from the available existing literatures, otherwise, we made suitable assumptions to carry out the simulations for illustration purposes. 17. The conclusion is too long. Paragraph one seems to be overelaborated. Other paragraphs should be simplified. Is there any literature support to your conclusions? Response: We have revised the whole conclusion part very carefully. Reviewer #2: Review report on the manuscript “Modeling and Analysis of Smoking and Alcoholism Dual Addiction Dynamics with Optimal Control Theory and Cost-Effectiveness” I have carefully read the paper, and it seems interesting. Therefore, the manuscript can be considered further for publication in PLOS ONE if the authors are willing to incorporate a MAJOR Revision. Here under are my specific comments on the manuscript: 1. It is strongly advised and it is the responsibility of the authors to check the whole manuscript and correct all the grammatical errors and typos. The manuscript is full of grammatical errors and typos. It is enough to recommend rejection if the authors fail to thoroughly proofread their revised manuscript. Response: We agree with this basic comment and we revised the full manuscript accordingly. 2. In the abstract, it is not clear on what control interventions were the optimal strategies and cost-effectiveness analysis carried on. Response: The study carried out cost-effectiveness analysis to compare the cost incurred when we applied each of the proposed strategies A to I and in the revised manuscript abstract section we explained as “The cost-effectiveness analysis shows that implementing all the protection (education) control measures simultaneously (i.e. implementing Strategy A) is the most cost-effective strategy” 3. The last sentence in the abstract should be split into simple sentences with clear information. Response: We re-wrote it again accordingly. 4. There are a number of compound sentences with no clear meanings throughout the manuscript. For instance, see the first sentence under the introduction section. I suggest that the authors split this kind of sentences into simple ones with clear meanings. Response: We revised accordingly. 5. There are a number of long sentences in the paper. For instance, the first sentence in the first paragraph on the second page is too long. The sentence should be split into simple and meaningful sentences. Response: We revised accordingly. 6. The literature review should be updated with the following related works: a) https://doi.org/10.1007/s40314-022-01760-2 b) https://www.lhscientificpublishing.com/Journals/articles/DOI-10.5890-JAND.2023.03.004.aspx Response: We have incorporated these up-to-date and related peer-reviewed published literatures to improve our revised manuscript. 7. Description of the parameters delta_1, delta_2, delta_3, rho_1, rho_2 and rho_3 being "modification parameters" as mentioned by the authors in Table 1 is not clear. The physical meanings of the parameters should be given. Response: We have given the right physical meanings of all the mentioned parameters in the revised manuscript accordingly. 8. theta_1 and theta_2 should be described better than just being modification parameters. Please, see the recommended articles in (6) for similar parameter descriptions. Response: We mean that θ_1 is the modification parameter that verify smoking and alcohol dual addicted individuals are more involved in the alcohol addiction dissemination process than the alcohol only addicted individuals. Similarly, we mean that θ_2 is the modification parameter that verify smoking and alcohol dual addicted individuals are more involved in the smoking addiction dissemination process than the smoking only addicted individuals. 9. In the flowchart in Figure 1, the rate of progression from P_S to C_SA is missing. The authors should fix this. Response: Sorry for our mistake not to incorporate the term ρ_2 λ_A in the model flow chart what we have considered in the derivative of the state variables P_S and C_(SA ) for the dynamical system (4). In the revised manuscript we have corrected this mistake. 10. The adjoint variables f_i,i=1,2,...,11 in Equation (21) and thereafter are different from their original definitions (with boldface). The authors should make corrections accordingly. Response: We have corrected accordingly. 11. What is th Attachments Attachment Submitted filename: RESPONSETOREVIEWRCOMMENTS.docx https://doi.org/10.1371/journal.pone.0309356.r002
26 Jul 2024 Decision Letter - Joshua Kiddy K. Asamoah, Editor PONE-D-24-23154R1Smoking and Alcoholism Dual Addiction Dissemination Model Analysis with Optimal Control Theory and Cost-EffectivenessPLOS ONE Dear Dr. Teklu, 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. ============================== ACADEMIC EDITOR: General comment The abstract and conclusion are well-written. However, the keywords should not contain words already in the title. Other comments. (1) The manuscript has a few grammatical errors and typos. The authors need to rectify these. (2) Please clearly state the novelty of the work in connection to the mathematical modelling of the disease. What new compartment(s) have the authors added, and why do they need to add those compartment(s)? (3) The authors should indicate in their motivation the new mathematical analysis used in studying this dynamics, which other researchers haven’t considered. (4) In the numerical section, the authors should improve on discussing the various Figures obtained and their impact on smoking and alcoholism control. I kindly request you to provide a thoroughly revised manuscript along with a point-by-point response delineating how you addressed my general and specific comments; I meant exactly that. As to the point-by-point response, revised text in different colours is necessary, but that is not sufficient to let me know that you modified any given issue; it is necessary to answer specifically HOW you addressed/changed each issue in the response letter. Please understand that I must request another revision/rejection of your manuscript if the revisions are inadequate. ============================== Please submit your revised manuscript by Sep 09 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, Joshua Kiddy K. Asamoah, PhD 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. [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: All comments have been addressed Reviewer #2: 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 #1: Yes Reviewer #2: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: N/A Reviewer #2: 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 #1: Yes Reviewer #2: 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: 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 #1: The authors have responded to many of my comments accurately. Notwithstanding this, kindly check these comments to improve the paper. 1. The paper still has some grammatical errors. Check the last statement in the abstract and also the entire paper. 2. The literature support for the assumptions should be cited before stating the assumptions. 3. Regarding my comment 8, your response indicated that similar works are done in [30-32], but you cited [38-40] instead in the article. Which one is the proper citation? 4. The manuscript still has a lot of formatting inaccuracies. Please work on them. Reviewer #2: The authors have carefully addressed all my comments to satisfaction. Thus, the manuscript can be considered further for publication by Plos One. ****** 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: Yes: Afeez Abidemi ******** [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.0309356.r003
Revision 2
2 Aug 2024 Author Response Dear Editor, we the authors of the manuscript entitled “Smoking and Alcoholism Dual Addiction Dissemination Model Analysis with Optimal Control Theory and Cost-Effectiveness” thanks all the editors and reviewers for their great contribution in the review process and sharing knowledge of real world problem dynamics. Dear, Sir we have the following point by point responses. Editor and Reviewers Comments and Authors Responses Editor Comments and Authors Responses The abstract and conclusion are well-written. However, the keywords should not contain words already in the title. Response: According to the comment given above, we removed some word from the previous manuscript and the keywords in the revised manuscript include: Smoking; Alcoholism; Smoking and Alcoholism Dual Addiction; Optimal Control Theory; Cost-Effectiveness, all are already in the title of the revised manuscript. Other comments: The manuscript has a few grammatical errors and typos. The authors need to rectify these. Response: According to the comment given to us we have read the whole manuscript again and again and corrected some grammatical errors we addressed in each page of the previous manuscript. Please clearly state the novelty of the work in connection to the mathematical modelling of the disease. What new compartment(s) have the authors added, and why do they need to add those compartment(s)? Response: Dear editor, whenever we the authors studied different co-infection models on infectious diseases and we reviewed various published sources carried out by different scholars on the transmission dynamics of co-infections of infectious diseases. Also, in the formulation of this proposed dual addiction model we reviewed different co-existence models, however, to the best of the our understanding no one is formulated and analyzed eleven compartmental co-infection model by considering a protection compartment against both infections with optimal control theory and cost-effectiveness analysis. In comparisons with other scholars’ co-existence (dual existence) mathematical modeling studies on infectious diseases or social behaviors the new compartments that incorporated in our formulated model are the protection compartment denoted by P and the compartment that contains individuals who are permanently dual addicted with both smoking and alcohol denoted by P_SA. We add these two compartments in our formulated model: To investigate the impacts of pre-exposure mechanism such as the impact of education protection mechanism on the dual addiction dissemination dynamics in the community. To understand the smoking and alcoholism dual addicted individuals behavior, the dual addiction dissemination health impact, economic impact in the community and to verify how these addictions have long run impact on individuals who are permanently dual addicted with both smoking and alcohol ( since they cannot rehabilitated from their dual addiction). The authors should indicate in their motivation the new mathematical analysis used in studying this dynamics, which other researchers haven’t considered. Response: From response of the comment 3 above we have explained that no alcohol addiction or smoking addiction or smoking and alcohol dual addiction mathematical model studies incorporated the protected group (protected compartment) against both addictions (by education), the permanently dual addicted group, optimal control theory and cost-effectiveness analysis in the dissemination dynamics of these addictions. Similarly, in case of mathematical analysis no smoking and alcoholism dual addiction mathematical modeling research studies analyzed the phenomenon of backward bifurcation. In the numerical section, the authors should improve on discussing the various Figures obtained and their impact on smoking and alcoholism control. Response: We have improved the discussions by showing the impacts of the proposed control measures by comparing with other strategies in each case and the result determined without applying any control strategy. *I kindly request you to provide a thoroughly revised manuscript along with a point-by-point response delineating how you addressed my general and specific comments; I meant exactly that. As to the point-by-point response, revised text in different colors is necessary, but that is not sufficient to let me know that you modified any given issue; it is necessary to answer specifically HOW you addressed/changed each issue in the response letter. Response: We revised according to the editor suggestions. Reviewer 1 Comments and Authors Responses The paper still has some grammatical errors. Check the last statement in the abstract and also the entire paper. Response: We have corrected some grammatical errors we addressed in each page of the previous manuscript. The literature support for the assumptions should be cited before stating the assumptions. Response: In page 5 of this revised manuscript, we made corrections and cited relevant studies for model assumptions before we started the assumptions. Regarding my comment 8, your response indicated that similar works are done in [30-32], but you cited [38-40] instead in the article. Which one is the proper citation? Response: Sorry for our mistake what we have done in the first revision process the according to the new reference arrangement in the first revision process the corrected citation should be [38-40]. Dear Sir, please consider the proper citation [38-41] for this revised manuscript. The manuscript still has a lot of formatting inaccuracies. Please work on them. Response: In the revised manuscript we have corrected various formatting inaccuracies Attachments Attachment Submitted filename: RESPONSESFORSECONDREVISSION.docx* https://doi.org/10.1371/journal.pone.0309356.r004
12 Aug 2024 Decision Letter - Joshua Kiddy K. Asamoah, Editor Smoking and Alcoholism Dual Addiction Dissemination Model Analysis with Optimal Control Theory and Cost-Effectiveness PONE-D-24-23154R2 Dear Dr. Teklu, 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. 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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) ******** 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 ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: 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 #1: 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 ****** 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 paper is currently in a good state to be accepted for publication subject to these considerations. 1. In the abstract, authors used the word "created". I suggest that word be changed since all mathematical models are modifications or extensions based on the existing SIR model propounded by Kermack and McKendrick in 1927. 2. The references are not meeting the standards of Plos One journal. This should be done. ****** 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 ******** https://doi.org/10.1371/journal.pone.0309356.r005
Formally Accepted
19 Aug 2024 Acceptance Letter - Joshua Kiddy K. Asamoah, Editor PONE-D-24-23154R2 PLOS ONE Dear Dr. Teklu, 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. Joshua Kiddy K. Asamoah Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0309356.r006

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