Mathematical Modeling of Carbon Dioxide Emissions with GDP Linkage: Sensitivity Analysis and Optimal Control Strategy

Mathematical Modeling of Carbon Dioxide Emissions with GDP Linkage: Sensitivity Analysis and Optimal Control Strategy | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Mathematical Modeling of Carbon Dioxide Emissions with GDP Linkage: Sensitivity Analysis and Optimal Control Strategy Hua Liu, Zhuoma Gangji, Yumei Wei, Jianhua Ye, Gang Ma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7295422/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Jan, 2026 Read the published version in Carbon Balance and Management → Version 1 posted 9 You are reading this latest preprint version Abstract Climate change and global warming are among the most significant issues that humanity is currently facing, and also among the issues that pose the greatest threats to all mankind. These issues are primarily driven by abnormal increases in greenhouse gas concentrations. Mathematical modeling serves as a powerful approach to analyze the dynamic patterns of atmospheric carbon dioxide. In this paper, we established a mathmetical model with four state variables to investigate the dynamic behavior of the interaction between atmospheric carbon dioxide, GDP, forest area and human population. Relevant theories were employed to analyze the system's boundedness and the stability of equilibrium points. The parameter values were estimated with the help of the actual data in China and numerical fitting was carried out to verify the results of the theoretical analysis. The sensitivity analysis of the compartments with respect to the model parameters was analyzed by using the Partial Rank Correlation Coefficient (PRCC) and the Latin Hypercube Sampling test. Apply the optimal control theory to regulate the atmospheric carbon dioxide level and provide the corresponding numerical fitting. Finally, corresponding discussions and suggestions were put forward with the help of the results of the theoretical analysis and numerical fitting. Mathematical Model Carbon dioxide(CO2) GDP Sensitivity analysis Optimal Control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Jan, 2026 Read the published version in Carbon Balance and Management → Version 1 posted Editorial decision: Revision requested 29 Sep, 2025 Reviews received at journal 18 Sep, 2025 Reviews received at journal 03 Sep, 2025 Reviewers agreed at journal 30 Aug, 2025 Reviewers agreed at journal 28 Aug, 2025 Reviewers invited by journal 28 Aug, 2025 Editor assigned by journal 24 Aug, 2025 Submission checks completed at journal 14 Aug, 2025 First submitted to journal 04 Aug, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7295422","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":509695982,"identity":"395dc263-7263-4f12-9d52-6e95020265e5","order_by":0,"name":"Hua Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYBACxgbmNoYPDAfAHAkitTC2Mc4gSQtQUxszD0lamPsPtj22bbsTbXCA+eBtHga7PMJ2zEhsN8458yx3wwG2ZGsehuRiIrQwtknnVBwGauExkwa6MLGBoBagw6QtDEBa+L8RqaUhsU2aAWILG5FaZiS2SfYA/TLzMJux5RyDZMJaDPsPH5P42XYnt+9488MbbyrsiNACV8EMIgwIqQcCeSLUjIJRMApGwUgHAI3RP1N39yQdAAAAAElFTkSuQmCC","orcid":"","institution":"Northwest Minzu University","correspondingAuthor":true,"prefix":"","firstName":"Hua","middleName":"","lastName":"Liu","suffix":""},{"id":509695983,"identity":"992266b9-9ff6-421a-9ede-97b1831bb9e4","order_by":1,"name":"Zhuoma Gangji","email":"","orcid":"","institution":"Northwest Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Zhuoma","middleName":"","lastName":"Gangji","suffix":""},{"id":509695984,"identity":"f1840fc4-7aba-4bdf-bb06-08c83ef10ff4","order_by":2,"name":"Yumei Wei","email":"","orcid":"","institution":"Northwest Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Yumei","middleName":"","lastName":"Wei","suffix":""},{"id":509695985,"identity":"543b31d0-137f-4be6-b041-9f1109656b04","order_by":3,"name":"Jianhua Ye","email":"","orcid":"","institution":"Northwest Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Jianhua","middleName":"","lastName":"Ye","suffix":""},{"id":509695986,"identity":"9e788a52-0a1b-4d4d-9809-2d1788c88902","order_by":4,"name":"Gang Ma","email":"","orcid":"","institution":"Northwest Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Gang","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2025-08-05 02:23:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7295422/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7295422/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s13021-025-00359-4","type":"published","date":"2026-01-02T15:57:01+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":99545204,"identity":"28b72f34-1d30-4a0d-8b8e-ae056bfc4c57","added_by":"auto","created_at":"2026-01-05 16:02:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":799175,"visible":true,"origin":"","legend":"","description":"","filename":"CarbondioxideandGDP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7295422/v1_covered_a91a6feb-3881-48a3-91e8-5acd3c82515f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mathematical Modeling of Carbon Dioxide Emissions with GDP Linkage: Sensitivity Analysis and Optimal Control Strategy","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"carbon-balance-and-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cbam","sideBox":"Learn more about [Carbon Balance and Management](https://cbmjournal.biomedcentral.com/)","snPcode":"13021","submissionUrl":"https://submission.nature.com/new-submission/13021/3","title":"Carbon Balance and Management","twitterHandle":"@BioMedCentral","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Mathematical Model, Carbon dioxide(CO2), GDP, Sensitivity analysis, Optimal Control","lastPublishedDoi":"10.21203/rs.3.rs-7295422/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7295422/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Climate change and global warming are among the most significant issues that humanity is currently facing, and also among the issues that pose the greatest threats to all mankind. 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