{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T07:22:42Z","timestamp":1781940162214,"version":"3.54.5"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T00:00:00Z","timestamp":1722211200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T00:00:00Z","timestamp":1722211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research, India","doi-asserted-by":"publisher","award":["09\/1051(12023)\/2021- EMR-I"],"award-info":[{"award-number":["09\/1051(12023)\/2021- EMR-I"]}],"id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006143","name":"Department of Science and Technology, Government of Kerala","doi-asserted-by":"publisher","award":["SR\/FST\/MS-I\/2021\/104"],"award-info":[{"award-number":["SR\/FST\/MS-I\/2021\/104"]}],"id":[{"id":"10.13039\/501100006143","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-024-66580-2","type":"journal-article","created":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T14:12:46Z","timestamp":1722262366000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Cholera disease dynamics with vaccination control using delay differential equation"],"prefix":"10.1038","volume":"14","author":[{"given":"Jaskirat Pal","family":"Singh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sachin","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali","family":"Akg\u00fcl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Murad Khan","family":"Hassani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,7,29]]},"reference":[{"key":"66580_CR1","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/0264-410X(88)90217-4","volume":"6","author":"I Joo","year":"1988","unstructured":"Joo, I. & Em\u00f6d, J. Adjuvant effect of deae-dextran on cholera vaccines. Vaccine 6, 233\u2013237. https:\/\/doi.org\/10.1016\/0264-410X(88)90217-4 (1988).","journal-title":"Vaccine"},{"key":"66580_CR2","first-page":"421","volume":"10","author":"R Pollitzer","year":"1954","unstructured":"Pollitzer, R. Cholera studies: 1. history of the disease. Bull. World Health Organ. 10, 421 (1954).","journal-title":"Bull. World Health Organ."},{"key":"66580_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.eclinm.2021.100753","volume":"32","author":"OB Hassan","year":"2021","unstructured":"Hassan, O. B. & Nellums, L. B. Cholera during covid-19: The forgotten threat for forcibly displaced populations. EClinicalMedicine 32, 100753. https:\/\/doi.org\/10.1016\/j.eclinm.2021.100753 (2021).","journal-title":"EClinicalMedicine"},{"key":"66580_CR4","unstructured":"Van\u00a0Heyningen, W. & Seal, J. Cholera: The american scientific experience, 1947\u20131980. boulder, co. Westview Press, 7, 95\u2013124, (1983)."},{"key":"66580_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.tmaid.2022.102423","author":"A Reda","year":"2022","unstructured":"Reda, A., Sah, R., Abdelaal, A., Shrestha, S. & Rodriguez-Morales, A. J. The emergence of cholera in multiple countries amidst current covid-19 pandemic: Situation and implications for public health and travel medicine. Travel Med. Infect. Dis.https:\/\/doi.org\/10.1016\/j.tmaid.2022.102423 (2022).","journal-title":"Travel Med. Infect. Dis."},{"key":"66580_CR6","doi-asserted-by":"publisher","first-page":"e01721","DOI":"10.1128\/mbio.01721-14","volume":"5","author":"M Eppinger","year":"2014","unstructured":"Eppinger, M. et al. Genomic epidemiology of the haitian cholera outbreak: A single introduction followed by rapid, extensive, and continued spread characterized the onset of the epidemic. MBio 5, e01721. https:\/\/doi.org\/10.1128\/mbio.01721-14 (2014).","journal-title":"MBio"},{"key":"66580_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1128\/microbiolspec.oh-0003-2012","volume":"1","author":"S Almagro-Moreno","year":"2013","unstructured":"Almagro-Moreno, S. & Taylor, R. K. Cholera: environmental reservoirs and impact on disease transmission. Microbiol. Spectr. 1, 1\u20132. https:\/\/doi.org\/10.1128\/microbiolspec.oh-0003-2012 (2013).","journal-title":"Microbiol. Spectr."},{"key":"66580_CR8","unstructured":"WHO. Cholera - global situation (2023)."},{"key":"66580_CR9","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/S0140-6736(03)15328-7","volume":"363","author":"S Da","year":"2004","unstructured":"Da, S. Cholera. Lancet 363, 223\u2013233. https:\/\/doi.org\/10.1016\/S0140-6736(03)15328-7 (2004).","journal-title":"Lancet"},{"issue":"3","key":"66580_CR10","doi-asserted-by":"publisher","first-page":"597","DOI":"10.4269\/ajtmh.12-0721","volume":"89","author":"A Jutla","year":"2013","unstructured":"Jutla, A. et al. Environmental factors influencing epidemic cholera. Am. Soc. Trop. Med. Hyg. 89(3), 597. https:\/\/doi.org\/10.4269\/ajtmh.12-0721 (2013).","journal-title":"Am. Soc. Trop. Med. Hyg."},{"key":"66580_CR11","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.jtbi.2012.12.021","volume":"324","author":"MC Eisenberg","year":"2013","unstructured":"Eisenberg, M. C., Robertson, S. L. & Tien, J. H. Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease. J. Theor. Biol. 324, 84\u2013102. https:\/\/doi.org\/10.1016\/j.jtbi.2012.12.021 (2013).","journal-title":"J. Theor. Biol."},{"key":"66580_CR12","unstructured":"WHO. Cholera (2022)."},{"key":"66580_CR13","unstructured":"GTFCC. Roadmap 2030 (2017)."},{"key":"66580_CR14","doi-asserted-by":"publisher","unstructured":"Bynum, W. In retrospect: On the mode of communication of cholera, https:\/\/doi.org\/10.1038\/495169a (2013).","DOI":"10.1038\/495169a"},{"key":"66580_CR15","doi-asserted-by":"publisher","first-page":"2358","DOI":"10.3390\/microorganisms10122358","volume":"10","author":"J Wang","year":"2022","unstructured":"Wang, J. Mathematical models for cholera dynamics-a review. Microorganisms 10, 2358. https:\/\/doi.org\/10.3390\/microorganisms10122358 (2022).","journal-title":"Microorganisms"},{"key":"66580_CR16","doi-asserted-by":"publisher","first-page":"4616","DOI":"10.1038\/s41598-024-55240-0","volume":"14","author":"KW Brhane","year":"2024","unstructured":"Brhane, K. W., Ahmad, A. G., Hina, H. & Emadifar, H. Mathematical modeling of cholera dynamics with intrinsic growth considering constant interventions. Sci. Rep. 14, 4616. https:\/\/doi.org\/10.1038\/s41598-024-55240-0 (2024).","journal-title":"Sci. Rep."},{"key":"66580_CR17","doi-asserted-by":"publisher","first-page":"1387","DOI":"10.1007\/s40808-022-01570-9","volume":"9","author":"B Gbadamosi","year":"2023","unstructured":"Gbadamosi, B. et al. Modeling the impact of optimal control measures on the dynamics of cholera. Model. Earth Syst. Environ. 9, 1387\u20131400. https:\/\/doi.org\/10.1007\/s40808-022-01570-9 (2023).","journal-title":"Model. Earth Syst. Environ."},{"key":"66580_CR18","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.cnsns.2016.10.007","volume":"45","author":"G-Q Sun","year":"2017","unstructured":"Sun, G.-Q. et al. Transmission dynamics of cholera: Mathematical modeling and control strategies. Commun. Nonlinear Sci. Numer. Simul. 45, 235\u2013244. https:\/\/doi.org\/10.1016\/j.cnsns.2016.10.007 (2017).","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"66580_CR19","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.jtbi.2012.02.006","volume":"301","author":"A Misra","year":"2012","unstructured":"Misra, A. & Singh, V. A delay mathematical model for the spread and control of water borne diseases. J. Theor. Biol. 301, 49\u201356. https:\/\/doi.org\/10.1016\/j.jtbi.2012.02.006 (2012).","journal-title":"J. Theor. Biol."},{"key":"66580_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112477","volume":"162","author":"S Rashid","year":"2022","unstructured":"Rashid, S., Jarad, F. & Alsharidi, A. K. Numerical investigation of fractional-order cholera epidemic model with transmission dynamics via fractal-fractional operator technique. Chaos, Solitons Fractals 162, 112477. https:\/\/doi.org\/10.1016\/j.chaos.2022.112477 (2022).","journal-title":"Chaos, Solitons Fractals"},{"key":"66580_CR21","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1142\/S1793048020500071","volume":"15","author":"T Nguiwa","year":"2020","unstructured":"Nguiwa, T., Justin, M., Moussa, D., Betchewe, G. & Mohamadou, A. Dynamic study of siqr-b fractional-order epidemic model of cholera with optimal control strategies in mayo-tsanaga department of cameroon far north region. Biophys. Rev. Lett. 15, 237\u2013273. https:\/\/doi.org\/10.1142\/S1793048020500071 (2020).","journal-title":"Biophys. Rev. Lett."},{"key":"66580_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2022.114969","volume":"423","author":"F \u00d6zk\u00f6se","year":"2023","unstructured":"\u00d6zk\u00f6se, F., Habbireeh, R. & \u015eenel, M. T. A novel fractional order model of sars-cov-2 and cholera disease with real data. J. Comput. Appl. Math. 423, 114969. https:\/\/doi.org\/10.1016\/j.cam.2022.114969 (2023).","journal-title":"J. Comput. Appl. Math."},{"key":"66580_CR23","doi-asserted-by":"publisher","first-page":"10927","DOI":"10.1038\/s41598-024-59640-0","volume":"14","author":"A Ahmad","year":"2024","unstructured":"Ahmad, A. et al. Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures. Sci. Rep. 14, 10927. https:\/\/doi.org\/10.1038\/s41598-024-59640-0 (2024).","journal-title":"Sci. Rep."},{"key":"66580_CR24","doi-asserted-by":"publisher","first-page":"11547","DOI":"10.1016\/j.amc.2012.04.085","volume":"218","author":"A Misra","year":"2012","unstructured":"Misra, A., Mishra, S., Pathak, A., Misra, P. & Naresh, R. Modeling the effect of time delay in controlling the carrier dependent infectious disease - cholera. Appl. Math. Comput. 218, 11547\u201311557. https:\/\/doi.org\/10.1016\/j.amc.2012.04.085 (2012).","journal-title":"Appl. Math. Comput."},{"key":"66580_CR25","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.mbs.2018.02.001","volume":"298","author":"OS Sisodiya","year":"2018","unstructured":"Sisodiya, O. S., Misra, O. & Dhar, J. Dynamics of cholera epidemics with impulsive vaccination and disinfection. Math. Biosci. 298, 46\u201357. https:\/\/doi.org\/10.1016\/j.mbs.2018.02.001 (2018).","journal-title":"Math. Biosci."},{"key":"66580_CR26","doi-asserted-by":"publisher","first-page":"3977","DOI":"10.1007\/s11071-023-09234-8","volume":"112","author":"W Ahmad","year":"2024","unstructured":"Ahmad, W. et al. Analytical and numerical explorations of optimal control techniques for the bi-modal dynamics of covid-19. Nonlinear Dyn. 112, 3977\u20134006. https:\/\/doi.org\/10.1007\/s11071-023-09234-8 (2024).","journal-title":"Nonlinear Dyn."},{"key":"66580_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.121094","volume":"234","author":"AIK Butt","year":"2023","unstructured":"Butt, A. I. K., Ahmad, W., Rafiq, M., Ahmad, N. & Imran, M. Computationally efficient optimal control analysis for the mathematical model of coronavirus pandemic. Expert Syst. Appl. 234, 121094. https:\/\/doi.org\/10.1016\/j.eswa.2023.121094 (2023).","journal-title":"Expert Syst. Appl."},{"key":"66580_CR28","volume-title":"Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications","author":"I Podlubny","year":"1998","unstructured":"Podlubny, I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Elsevier, 1998)."},{"key":"66580_CR29","volume-title":"Fractional integrals and derivatives","author":"SG Samko","year":"1993","unstructured":"Samko, S. G. et al. Fractional integrals and derivatives Vol. 1 (Gordon and Breach science publishers, 1993)."},{"key":"66580_CR30","doi-asserted-by":"publisher","DOI":"10.1142\/S0218348X23400960","author":"JP Singh","year":"2023","unstructured":"Singh, J. P., Kumar, S., Baleanu, D. & Nisar, K. S. Monkeypox viral transmission dynamics and fractional order modeling with vaccination intervention. Fractalshttps:\/\/doi.org\/10.1142\/S0218348X23400960 (2023).","journal-title":"Fractals"},{"key":"66580_CR31","first-page":"1","volume":"1","author":"S Bhalekar","year":"2011","unstructured":"Bhalekar, S. & Daftardar-Gejji, V. A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order. J. Fract. Calc. Appl 1, 1\u20139 (2011).","journal-title":"J. Fract. Calc. Appl"},{"key":"66580_CR32","doi-asserted-by":"publisher","unstructured":"Van\u00a0den Driessche, P. & Watmough, J. Further notes on the basic reproduction number. Mathematical epidemiology 159\u2013178, https:\/\/doi.org\/10.1007\/978-3-540-78911-6_6 (2008).","DOI":"10.1007\/978-3-540-78911-6_6"},{"key":"66580_CR33","volume-title":"Mathematical epidemiology of infectious diseases: model building, analysis and interpretation","author":"O Diekmann","year":"2000","unstructured":"Diekmann, O. & Heesterbeek, J. A. P. Mathematical epidemiology of infectious diseases: model building, analysis and interpretation Vol. 5 (John Wiley & Sons, 2000)."},{"key":"66580_CR34","unstructured":"Abbas, S. Existence of solutions to fractional order ordinary and delay differential equations and applications. Electronic Journal of Differential Equations (EJDE)[electronic only]2011 (2011)."},{"key":"66580_CR35","volume-title":"Introduction to functional differential equations","author":"JK Hale","year":"2013","unstructured":"Hale, J. K. & Lunel, S. M. V. Introduction to functional differential equations Vol. 99 (Springer Science & Business Media, 2013)."},{"key":"66580_CR36","volume-title":"Theory and applications of Hopf bifurcation","author":"BD Hassard","year":"1981","unstructured":"Hassard, B. D., Kazarinoff, N. D., Wan, Y.-H. & Wan, Y.-H. Theory and applications of Hopf bifurcation Vol. 41 (CUP Archive, 1981)."},{"key":"66580_CR37","first-page":"863","volume":"10","author":"S Ruan","year":"2003","unstructured":"Ruan, S. & Wei, J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous Discrete and Impulsive Systems Series A 10, 863\u2013874 (2003).","journal-title":"Dynamics of Continuous Discrete and Impulsive Systems Series A"},{"key":"66580_CR38","first-page":"519","volume":"20","author":"X Lin","year":"2012","unstructured":"Lin, X. & Wang, H. Stability analysis of delay differential equations with two discrete delays. Can. Appl. Math. Q. 20, 519\u2013533 (2012).","journal-title":"Can. Appl. Math. Q."},{"key":"66580_CR39","unstructured":"Inc., T. M. MATLAB version: 9.14.0 (R2023a) (2023)."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-66580-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-66580-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-66580-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T14:15:07Z","timestamp":1722262507000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-66580-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,29]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["66580"],"URL":"https:\/\/doi.org\/10.1038\/s41598-024-66580-2","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,29]]},"assertion":[{"value":"15 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"17421"}}