{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T14:30:05Z","timestamp":1787668205679,"version":"build-2736575974"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1007\/s12190-026-02870-4","type":"journal-article","created":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T10:05:56Z","timestamp":1786529156000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal control and sensitivity analysis of smoking epidemic model"],"prefix":"10.1007","volume":"72","author":[{"given":"Tariq","family":"Hassan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9885-5685","authenticated-orcid":false,"given":"Pattrawut","family":"Chansangiam","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,12]]},"reference":[{"key":"2870_CR1","unstructured":"World Health Organization: WHO report on the global tobacco epidemic: the MPOWER package, World Health Organization, (2008). https:\/\/iris.who.int\/handle\/10665\/4381"},{"key":"2870_CR2","unstructured":"Institute for Health Metrics and Evaluation Thailand. September 21, 2021. http:\/\/www.healthdata.org\/thailand"},{"issue":"12","key":"2870_CR3","doi-asserted-by":"publisher","first-page":"2400726","DOI":"10.1002\/adts.202400726","volume":"7","author":"P.A. Naik","year":"2024","unstructured":"Naik, P.A., Yeolekar, B.M., Qureshi, S., Manhas, N., Ghoreishi, M., Yeolekar, M., Huang, Z.: Global analysis of a fractional-order hepatitis B virus Model under immune response in the presence of cytokines. Adv. Theory Simulations 7(12), 2400726 (2024). https:\/\/doi.org\/10.1002\/adts.202400726","journal-title":"Adv. Theory Simulations"},{"key":"2870_CR4","doi-asserted-by":"publisher","first-page":"101047","DOI":"10.1016\/j.padiff.2024.101047","volume":"13","author":"M. Farman","year":"2025","unstructured":"Farman, M., Hincal, E., Naik, P.A., Hasan, A., Sambas, A., Nisar, K.S.: A sustainable method for analyzing and studying the fractional-order panic spreading caused by the COVID-19 pandemic. Partial Diffe. Equ. Appl. Math 13, 101047 (2025). https:\/\/doi.org\/10.1016\/j.padiff.2024.101047","journal-title":"Partial Differ Equations Appl Math"},{"issue":"1","key":"2870_CR5","doi-asserted-by":"publisher","first-page":"24963","DOI":"10.1038\/s41598-024-75644-2","volume":"14","author":"P.A. Naik","year":"2024","unstructured":"Naik, P.A., Farman, M., Jamil, K., Nisar, K.S., Hashmi, M.A., Huang, Z.: Modeling and analysis using piecewise hybrid fractional operator in time scale measure for ebola virus epidemics under mittag-leffler kernel. Sci. Rep. 14(1), 24963 (2024). https:\/\/doi.org\/10.1038\/s41598-024-75644-2","journal-title":"Sci. Rep."},{"key":"2870_CR6","doi-asserted-by":"publisher","first-page":"108306","DOI":"10.1016\/j.cmpb.2024.108306","volume":"254","author":"P.A. Naik","year":"2024","unstructured":"Naik, P.A., Yavuz, M., Qureshi, S., Owolabi, K.M., Soomro, A., Ganie, A.H.: Memory impacts in hepatitis C: a global analysis of a fractional-order model with an effective treatment. Comput. Methods Programs Biomed. 254, 108306 (2024). https:\/\/doi.org\/10.1016\/j.cmpb.2024.108306","journal-title":"Comput. Methods Programs Biomed."},{"issue":"2","key":"2870_CR7","first-page":"403","volume":"34","author":"G. Zaman","year":"2011","unstructured":"Zaman, G.: Qualitative behavior of giving up smoking models. Bull. Malays. Math. Sci. Soc. Second. Ser. 34(2), 403\u2013415 (2011). http:\/\/eudml.org\/doc\/244432","journal-title":"Bull Malays Math Sci Soc Second Ser"},{"issue":"7","key":"2870_CR8","doi-asserted-by":"publisher","first-page":"5326","DOI":"10.1016\/j.apm.2012.10.005","volume":"37","author":"A. Zeb","year":"2013","unstructured":"Zeb, A., Zaman, G., Momani, S.: Square-root dynamics of a giving up smoking model. Appl. Math. Modell. 37(7), 5326\u20135334 (2013). https:\/\/doi.org\/10.1016\/j.apm.2012.10.005","journal-title":"Appl. Math. Modell."},{"key":"2870_CR9","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.amc.2019.01.053","volume":"354","author":"G. Rahman","year":"2019","unstructured":"Rahman, G., Agarwal, R.P., Din, Q.: Mathematical analysis of giving up smoking model via harmonic mean type incidence rate. Appl. Math. Comput. 354, 128\u2013148 (2019). https:\/\/doi.org\/10.1016\/j.amc.2019.01.053","journal-title":"Appl. Math. Comput."},{"key":"2870_CR10","doi-asserted-by":"publisher","first-page":"109132","DOI":"10.1016\/j.mbs.2023.109132","volume":"368","author":"S. Zhang","year":"2024","unstructured":"Zhang, S., Meng, Y., Chakraborty, A.K., Wang, H.: Controlling smoking: a smoking epidemic model with different smoking degrees in deterministic and stochastic environments. Math. Biosci. 368, 109132 (2024). https:\/\/doi.org\/10.1016\/j.mbs.2023.109132","journal-title":"Math Biosci."},{"issue":"1","key":"2870_CR11","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1140\/epjp\/s13360-020-00979-4","volume":"136","author":"T. Hussain","year":"2021","unstructured":"Hussain, T., Awan, A.U., Abro, K.A., Ozair, M., Manzoor, M.: A mathematical and parametric study of epidemiological smoking model: a deterministic stability and optimality for solutions. Eur. Phys. J. Plus. 136(1), 11 (2021). https:\/\/doi.org\/10.1140\/epjp\/s13360-020-00979-4","journal-title":"Eur Phys J Plus"},{"issue":"1","key":"2870_CR12","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/s12190-020-01402-y","volume":"65","author":"P. Harvim","year":"2021","unstructured":"Harvim, P., Zhang, H., Georgescu, P., Zhang, L.: Cigarette smoking on college campuses: an epidemical modelling approach. J. Appl. Math. Comput. 65(1), 515\u2013540 (2021). https:\/\/doi.org\/10.1007\/s12190-020-01402-y","journal-title":"J. Appl. Math. Comput."},{"issue":"2","key":"2870_CR13","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1016\/j.amc.2007.05.012","volume":"195","author":"O. Sharomi","year":"2008","unstructured":"Sharomi, O., Gumel, A.B.: Curtailing smoking dynamics: a mathematical modeling approach. Appl. Math. Comput. 195(2), 475\u2013499 (2008). https:\/\/doi.org\/10.1016\/j.amc.2007.05.012","journal-title":"Appl. Math. Comput."},{"issue":"4","key":"2870_CR14","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.drugpo.2011.05.003","volume":"22","author":"F. Guerrero","year":"2011","unstructured":"Guerrero, F., Santonja, F.J., Villanueva, R.J.: Analysing the Spanish smoke-free legislation of 2006: a new method to quantify its impact using a dynamic model. Int. J. Drug. Policy 22(4), 247\u2013251 (2011). https:\/\/doi.org\/10.1016\/j.drugpo.2011.05.003","journal-title":"Int. J. Drug. Policy"},{"key":"2870_CR15","unstructured":"World Health Organization: Global Adult Tobacco Survey (GATS). (2020). https:\/\/www.who.int"},{"issue":"1","key":"2870_CR16","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1186\/s13104-018-3574-4","volume":"11","author":"J. Mushanyu","year":"2018","unstructured":"Mushanyu, J.: Role of imitation and limited rehabilitation capacity on the spread of drug abuse. BMC. Res. Notes. 11(1), 493 (2018). https:\/\/doi.org\/10.1186\/s13104-018-3574-4","journal-title":"BMC Res Notes"},{"key":"2870_CR17","doi-asserted-by":"publisher","first-page":"8673020","DOI":"10.1155\/2021\/8673020Digital","volume":"1","author":"O. Khyar","year":"2021","unstructured":"Khyar, O., Danane, J., Allali, K.: Mathematical analysis and optimal control of giving up the smoking model. Int. J. Differ. Equations. 1, 8673020 (2021). https:\/\/doi.org\/10.1155\/2021\/8673020Digital","journal-title":"Int J Differ Equations"},{"key":"2870_CR18","doi-asserted-by":"crossref","unstructured":"La Salle, J.P.: The stability of dynamical systems. Soc. Ind. Appl. Math. (1976). https:\/\/epubs.siam.org\/doi\/book\/10.1137\/1.9781611970432","DOI":"10.1137\/1.9781611970432"},{"key":"2870_CR19","doi-asserted-by":"publisher","unstructured":"Butler, G., Freedman, H.I., Waltman, P.: Uniformly persistent systems. In: Proceedings of the American Mathematical Society, pp. 425\u2013430. (1986). https:\/\/doi.org\/10.1090\/S0002-9939-1986-0822433-4","DOI":"10.1090\/S0002-9939-1986-0822433-4"},{"key":"2870_CR20","doi-asserted-by":"publisher","unstructured":"Sumit Nandi, S., Priti KumarRoy, A.: Insight of viral infection of jatropha curcas plant (future Fue1): a control based mathematical study. 3(4) (2011). https:\/\/doi.org\/10.3724\/SP.J.1160.2011.00366","DOI":"10.3724\/SP.J.1160.2011.00366"},{"key":"2870_CR21","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1016\/j.amc.2015.09.012","volume":"271","author":"S. Khajanchi","year":"2015","unstructured":"Khajanchi, S., Ghosh, D.: The combined effects of optimal control in cancer remission. Appl. Math. Comput. 271, 375\u2013388 (2015). https:\/\/doi.org\/10.1016\/j.amc.2015.09.012","journal-title":"Appl. Math. Comput."},{"key":"2870_CR22","doi-asserted-by":"publisher","unstructured":"Lenhart, S., Workman, J.T.: Optimal control applied to biological models. Chapman Hall\/CRC (2007). https:\/\/doi.org\/10.1201\/9781420011418","DOI":"10.1201\/9781420011418"},{"issue":"2","key":"2870_CR23","doi-asserted-by":"publisher","first-page":"361","DOI":"10.3934\/mbe.2004.1.361","volume":"1","author":"C. Castillo-Chavez","year":"2004","unstructured":"Castillo-Chavez, C., Song, B.: Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1(2), 361 (2004). https:\/\/doi.org\/10.3934\/mbe.2004.1.361","journal-title":"Math. Biosci. Eng."},{"issue":"2","key":"2870_CR24","doi-asserted-by":"publisher","first-page":"6005","DOI":"10.29020\/nybg.ejpam.v18i2.6005","volume":"18","author":"M.S. Arif","year":"2025","unstructured":"Arif, M.S.: Numerical analysis of deterministic and stochastic Model of COVID-19 Co-infection with influenza. Eur. J. Pure Appl. Math. 18(2), 6005\u20136005 (2025). https:\/\/doi.org\/10.29020\/nybg.ejpam.v18i2.6005","journal-title":"Eur. J. Pure Appl. Math."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-026-02870-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-026-02870-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-026-02870-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T13:57:38Z","timestamp":1787666258000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-026-02870-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":24,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["2870"],"URL":"https:\/\/doi.org\/10.1007\/s12190-026-02870-4","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"3 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 August 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 August 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare there are no conflicts of interest.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"217"}}