{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T16:37:11Z","timestamp":1791823031589,"version":"4.3.4"},"reference-count":65,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T00:00:00Z","timestamp":1760659200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T00:00:00Z","timestamp":1760659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-025-20191-7","type":"journal-article","created":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:45:57Z","timestamp":1760712357000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Analysis of fractional-order model for the transmission dynamics of malaria via Caputo\u2013Fabrizio and Atangana\u2013Baleanu operators"],"prefix":"10.1038","volume":"15","author":[{"given":"Benedict Celestine","family":"Agbata","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Raimonda","family":"Dervishi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehmet","family":"G\u00fcm\u00fc\u015f","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aseel","family":"Smerat","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Godwin Christopher Ezike","family":"Mbah","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,10,17]]},"reference":[{"key":"20191_CR1","unstructured":"Global Fund. Results Report 2024: Malaria investment impact and trends. The Global Fund. Retrieved from https:\/\/www.theglobalfund.org\/media\/15029\/core_2024-results-malaria_report_en.pdf (2024)."},{"key":"20191_CR2","unstructured":"World Health Organization. World malaria report 2024: Reinvigorated global efforts needed to curb rising malaria threat. Retrieved from https:\/\/www.who.int\/teams\/global-malaria-programme\/reports\/world-malaria-report-2024 (2024)."},{"key":"20191_CR3","unstructured":"World Health Organization.. Malaria vaccines (RTS,S and R21). Retrieved from https:\/\/www.who.int\/news-room\/questions-and-answers\/item\/q-a-on-rts-s-malaria-vaccine (2024)"},{"key":"20191_CR4","doi-asserted-by":"publisher","unstructured":"Brown, B. J. et al. Data-driven malaria prevalence prediction in large densely-populated urban holoendemic sub-Saharan West Africa: Harnessing machine learning approaches and 22 years of prospectively collected data. arXiv. https:\/\/doi.org\/10.48550\/arXiv.1906.07502 (2019).","DOI":"10.48550\/arXiv.1906.07502"},{"issue":"6","key":"20191_CR5","doi-asserted-by":"publisher","first-page":"1027","DOI":"10.1007\/s15010-024-02196-y","volume":"52","author":"M Chutiyami","year":"2024","unstructured":"Chutiyami, M. et al. Malaria vaccine efficacy, safety, and community perception in Africa: A scoping review of recent empirical studies. Infection 52(6), 1027\u20131042. https:\/\/doi.org\/10.1007\/s15010-024-02196-y (2024).","journal-title":"Infection"},{"key":"20191_CR6","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1186\/s12887-024-05135-w","volume":"24","author":"I Isiko","year":"2024","unstructured":"Isiko, I. et al. Determinants of malaria spread among under-five children in Nigeria: Results from a 2021 Nigerian malaria indicator cross-sectional survey. BMC Pediatr. 24, 646. https:\/\/doi.org\/10.1186\/s12887-024-05135-w (2024).","journal-title":"BMC Pediatr."},{"key":"20191_CR7","unstructured":"CDC. Malaria Vaccines \u2013 Public Health Strategy. Centers for Disease Control and Prevention. Retrieved from https:\/\/www.cdc.gov\/malaria\/php\/public-health-strategy\/malaria-vaccines.html (2024)."},{"key":"20191_CR8","unstructured":"Le Monde. Lutte contre le paludisme\u00a0: une nouvelle r\u00e9sistance aux traitements standards observ\u00e9e chez les enfants. Retrieved https:\/\/www.lemonde.fr\/sciences\/article\/2024\/11\/20\/traitements-standards-observee-chez-les-enfants_6404172_1650684.html (2025)."},{"key":"20191_CR9","unstructured":"World Health Organization. African health leaders and global partners unite to confront rising threat of antimalarial drug resistance. WHO News. Retrieved https:\/\/www.who.int\/news\/item\/20-05-2025-african-health-leaders-and-global-partners (2025)."},{"issue":"1","key":"20191_CR10","doi-asserted-by":"publisher","first-page":"65","DOI":"10.21608\/ejmaa.2019.312741","volume":"7","author":"SI Onah","year":"2019","unstructured":"Onah, S. I., Collins, O. C., Okoye, C. & Mbah, G. C. E. Dynamics and control measures for malaria using a mathematical epidemiological model. Electron. J. Math. Anal. Appl. 7(1), 65\u201373. https:\/\/doi.org\/10.21608\/ejmaa.2019.312741 (2019).","journal-title":"Electron. J. Math. Anal. Appl."},{"issue":"3","key":"20191_CR11","doi-asserted-by":"publisher","first-page":"173","DOI":"10.3347\/kjp.2022.60.3.173","volume":"60","author":"DE Nwele","year":"2022","unstructured":"Nwele, D. E., Onyali, I. O., Iwueze, M. O., Elom, M. O. & Uguru, O. E. S. Malaria endemicity in the rural communities of Ebonyi State, Nigeria. Korean J. Parasitol. 60(3), 173\u2013179. https:\/\/doi.org\/10.3347\/kjp.2022.60.3.173 (2022).","journal-title":"Korean J. Parasitol."},{"key":"20191_CR12","unstructured":"Lancet Microbe.. WHO world malaria report 2024. The Lancet Microbe. Retrieved from https:\/\/www.thelancet.com\/journals\/lanmic\/article\/PIIS2666-5247(25)00001-1\/fulltext (2025)"},{"issue":"1","key":"20191_CR13","doi-asserted-by":"publisher","first-page":"82","DOI":"10.48185\/jmam.v6i1.1432","volume":"6","author":"EC Duru","year":"2025","unstructured":"Duru, E. C., Anyanwu, M. C. & Mbah, G. C. E. Mathematical analysis of a malaria model with vaccination, treatment, and vector control using sterile-insect technique. J. Math. Anal. Model. 6(1), 82\u2013106. https:\/\/doi.org\/10.48185\/jmam.v6i1.1432 (2025).","journal-title":"J. Math. Anal. Model."},{"issue":"5","key":"20191_CR14","doi-asserted-by":"publisher","DOI":"10.1136\/bmjgh-2022-011294","volume":"8","author":"OI Adelaja","year":"2023","unstructured":"Adelaja, O. I., Rudge, J. W. & Banerjee, A. Spatial and temporal trends of malaria in Nigeria: A sub-national analysis of surveillance data. BMJ Glob. Health 8(5), e011294. https:\/\/doi.org\/10.1136\/bmjgh-2022-011294 (2023).","journal-title":"BMJ Glob. Health"},{"issue":"1","key":"20191_CR15","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.healthpol.2008.09.012","volume":"90","author":"TA Okeke","year":"2009","unstructured":"Okeke, T. A. & Uzochukwu, B. S. C. Improving malaria treatment services in Nigeria: An evaluation of strategies for improving prompt access and reducing health inequities. Health Policy 90(1), 72\u201379. https:\/\/doi.org\/10.1016\/j.healthpol.2008.09.012 (2009).","journal-title":"Health Policy"},{"issue":"3","key":"20191_CR16","first-page":"265","volume":"37","author":"IO Ajayi","year":"2008","unstructured":"Ajayi, I. O. & Falade, C. O. Pre-hospital treatment of febrile illness in children attending the general outpatient clinic, University College Hospital, Ibadan, Nigeria. Afr. J. Med. Med. Sci. 37(3), 265\u2013271 (2008).","journal-title":"Afr. J. Med. Med. Sci."},{"issue":"1","key":"20191_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2478\/bile-2025-0001","volume":"62","author":"EC Duru","year":"2025","unstructured":"Duru, E. C. & Mbah, G. C. E. Approximate solution for a malaria model using the homotopy analysis method. Biometrical Lett. 62(1), 1\u201327. https:\/\/doi.org\/10.2478\/bile-2025-0001 (2025).","journal-title":"Biometrical Lett."},{"issue":"1","key":"20191_CR18","doi-asserted-by":"publisher","first-page":"79","DOI":"10.59292\/bulletinbiomath.1711811","volume":"3","author":"EC Duru","year":"2025","unstructured":"Duru, E. C., Anyanwu, M. C. & Mbah, G. C. E. A mathematical model to investigate the effect of misdiagnosis and wrong treatment in the co-circulation and co-infection of malaria and Zika virus disease. Bull. Biomath. 3(1), 79\u2013110. https:\/\/doi.org\/10.59292\/bulletinbiomath.1711811 (2025).","journal-title":"Bull. Biomath."},{"issue":"1","key":"20191_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s12936-016-1209-5","volume":"15","author":"CC Okeke","year":"2016","unstructured":"Okeke, C. C., Umeokonkwo, C. D., Ifeadike, C. O. & Ubajaka, C. Improving malaria diagnosis and treatment in under-five children in Nigeria: A cross-sectional study of primary health care facilities. Malar. J. 15(1), 1\u20139. https:\/\/doi.org\/10.1186\/s12936-016-1209-5 (2016).","journal-title":"Malar. J."},{"issue":"4","key":"20191_CR20","doi-asserted-by":"publisher","first-page":"115","DOI":"10.3923\/aje.2012.115.123","volume":"5","author":"LM Samdi","year":"2012","unstructured":"Samdi, L. M., Ajayi, J. A., Oguche, S. & Ayanlade, A. Climate change and malaria transmission dynamics in Nigeria: A review. Asian J. Epidemiol. 5(4), 115\u2013123. https:\/\/doi.org\/10.3923\/aje.2012.115.123 (2012).","journal-title":"Asian J. Epidemiol."},{"key":"20191_CR21","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1186\/1475-2875-6-145","volume":"6","author":"OA Mokuolu","year":"2007","unstructured":"Mokuolu, O. A., Okoronko, U., Adedoyin, O. T. & Afolabi, B. B. Effectiveness of a community-based intervention to increase ITN use among children under five in Nigeria. Malar. J. 6, 145. https:\/\/doi.org\/10.1186\/1475-2875-6-145 (2007).","journal-title":"Malar. J."},{"key":"20191_CR22","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/708197","volume":"2013","author":"BSC Uzochukwu","year":"2013","unstructured":"Uzochukwu, B. S. C., Onwujekwe, O. E., Uguru, N. P. & Okwuosa, C. The challenge of bridging the gap between evidence and policy in malaria control in Nigeria. Malaria Res. Treat. 2013, 708197. https:\/\/doi.org\/10.1155\/2013\/708197 (2013).","journal-title":"Malaria Res. Treat."},{"issue":"1","key":"20191_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/16583655.2019.1700972","volume":"14","author":"KA Adepoju","year":"2020","unstructured":"Adepoju, K. A. & Olaniyan, O. Mathematical modelling and optimal control of malaria transmission dynamics. J. Taibah Univ. Sci. 14(1), 1\u201313. https:\/\/doi.org\/10.1080\/16583655.2019.1700972 (2020).","journal-title":"J. Taibah Univ. Sci."},{"issue":"2","key":"20191_CR24","doi-asserted-by":"publisher","first-page":"41","DOI":"10.47260\/jamb\/1224","volume":"12","author":"AB Musa","year":"2022","unstructured":"Musa, A. B. & Luka, Y. Modelling the impact of vector control and vaccination on malaria dynamics in Nigeria. J. Appl. Math. Bioinform. 12(2), 41\u201360. https:\/\/doi.org\/10.47260\/jamb\/1224 (2022).","journal-title":"J. Appl. Math. Bioinform."},{"issue":"6","key":"20191_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1051\/mmnp\/2022023","volume":"17","author":"TT Yusuf","year":"2022","unstructured":"Yusuf, T. T., Benyah, F. & Okosun, K. O. A fractional-order model for the transmission dynamics of malaria with Caputo derivatives. Math. Model. Nat. Phenomena 17(6), 1\u201320. https:\/\/doi.org\/10.1051\/mmnp\/2022023 (2022).","journal-title":"Math. Model. Nat. Phenomena"},{"issue":"1","key":"20191_CR26","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1007\/s11071-021-06522-1","volume":"106","author":"CN Ngonghala","year":"2021","unstructured":"Ngonghala, C. N., Iboi, E. A. & Gumel, A. B. Mathematical assessment of the role of environmental interventions in malaria transmission dynamics using fractional calculus. Nonlinear Dyn. 106(1), 537\u2013559. https:\/\/doi.org\/10.1007\/s11071-021-06522-1 (2021).","journal-title":"Nonlinear Dyn."},{"key":"20191_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.113225","volume":"169","author":"A Omame","year":"2023","unstructured":"Omame, A., Okuonghae, D. & Okyere, E. A fractional-order malaria model with treatment and relapse: Analysis and optimal control. Chaos Solitons Fract. 169, 113225. https:\/\/doi.org\/10.1016\/j.chaos.2022.113225 (2023).","journal-title":"Chaos Solitons Fract."},{"key":"20191_CR28","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/3839240","volume":"2020","author":"D Kumar","year":"2020","unstructured":"Kumar, D. & Agrawal, O. P. A fractional mathematical model of malaria with a generalized Mittag-Leffler kernel. Comput. Math. Methods Med. 2020, 3839240. https:\/\/doi.org\/10.1155\/2020\/3839240 (2020).","journal-title":"Comput. Math. Methods Med."},{"issue":"1","key":"20191_CR29","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1186\/s13662-024-04321-y","volume":"2024","author":"A Abdelrazec","year":"2024","unstructured":"Abdelrazec, A., Elaiw, A. M. & Mahdy, A. M. Fractional-order malaria model with vaccination and vector control using Caputo-Fabrizio derivative. Adv. Differ. Equ. 2024(1), 45. https:\/\/doi.org\/10.1186\/s13662-024-04321-y (2024).","journal-title":"Adv. Differ. Equ."},{"issue":"3","key":"20191_CR30","doi-asserted-by":"publisher","first-page":"1677","DOI":"10.1016\/j.aej.2020.04.020","volume":"59","author":"NH Sweilam","year":"2020","unstructured":"Sweilam, N. H., Al-Mekhlafi, S. M. & Albalawi, A. O. Optimal control for a fractional order malaria transmission dynamics mathematical model. Alex. Eng. J. 59(3), 1677\u20131692. https:\/\/doi.org\/10.1016\/j.aej.2020.04.020 (2020).","journal-title":"Alex. Eng. J."},{"key":"20191_CR31","doi-asserted-by":"publisher","DOI":"10.1177\/10775463251320258","author":"A Boulkroune","year":"2025","unstructured":"Boulkroune, A., Zouari, F. & Boubellouta, A. Adaptive fuzzy control for practical fixed-time synchronization of fractional-order chaotic systems. Nonlinear Dyn. https:\/\/doi.org\/10.1177\/10775463251320258 (2025).","journal-title":"Nonlinear Dyn."},{"key":"20191_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neucom.2019.05.045","volume":"358","author":"F Zouari","year":"2019","unstructured":"Zouari, F. Neural network-based adaptive backstepping dynamic surface control of drug dosage regimens in cancer treatment. Neurocomputing 358, 1\u201311. https:\/\/doi.org\/10.1016\/j.neucom.2019.05.045 (2019).","journal-title":"Neurocomputing"},{"issue":"2","key":"20191_CR33","doi-asserted-by":"publisher","first-page":"104","DOI":"10.3390\/fractalfract9020104","volume":"9","author":"F Gassem","year":"2025","unstructured":"Gassem, F. et al. Nonlinear fractional evolution control modeling via power non-local kernels: A generalization of Caputo-Fabrizio, Atangana-Baleanu, and Hattaf derivatives. Fract. Fract. 9(2), 104. https:\/\/doi.org\/10.3390\/fractalfract9020104 (2025).","journal-title":"Fract. Fract."},{"key":"20191_CR34","doi-asserted-by":"publisher","first-page":"111030","DOI":"10.1016\/j.chaos.2021.111030","volume":"148","author":"H Khan","year":"2021","unstructured":"Khan, H. et al. A fractional order COVID-19 epidemic model with Mittag-Leffler kernel. Chaos Solitons Fract. 148, 111030. https:\/\/doi.org\/10.1016\/j.chaos.2021.111030 (2021).","journal-title":"Chaos Solitons Fract."},{"issue":"5","key":"20191_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.asej.2024.102646","volume":"15","author":"H Khan","year":"2024","unstructured":"Khan, H., Alzabut, J., G\u00f3mez-Aguilar, J. F. & Alkhazan, A. Essential criteria for existence of solution of a modified-ABC fractional order smoking model. Ain Shams Eng. J. 15(5), 102646. https:\/\/doi.org\/10.1016\/j.asej.2024.102646 (2024).","journal-title":"Ain Shams Eng. J."},{"key":"20191_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2023.107030","volume":"54","author":"J Alzabut","year":"2023","unstructured":"Alzabut, J., Dhineshbabu, R., Selvam, A. G. M., G\u00f3mez-Aguilar, J. F. & Khan, H. Existence, uniqueness and synchronization of a fractional tumor growth model in discrete time with numerical results. Results Phys. 54, 107030. https:\/\/doi.org\/10.1016\/j.rinp.2023.107030 (2023).","journal-title":"Results Phys."},{"key":"20191_CR37","doi-asserted-by":"publisher","first-page":"12211","DOI":"10.1038\/s41598-024-62386-4(Nature)","volume":"14","author":"A Khan","year":"2024","unstructured":"Khan, A., Shah, K., Abdeljawad, T. & Amacha, I. Fractal fractional model for tuberculosis: Existence and numerical solutions. Sci. Rep. 14, 12211. https:\/\/doi.org\/10.1038\/s41598-024-62386-4(Nature) (2024).","journal-title":"Sci. Rep."},{"issue":"1","key":"20191_CR38","doi-asserted-by":"publisher","first-page":"214","DOI":"10.3934\/nhm.2024010","volume":"19","author":"Eiman","year":"2024","unstructured":"Eiman, Shah, K., Sarwar, M. & Abdeljawad, T. On rotavirus infectious disease model using piecewise modified ABC fractional order derivative. Netw. Heterogeneous Media 19(1), 214\u2013234. https:\/\/doi.org\/10.3934\/nhm.2024010 (2024).","journal-title":"Netw. Heterogeneous Media"},{"issue":"2","key":"20191_CR39","doi-asserted-by":"publisher","first-page":"2440010","DOI":"10.1142\/S0218348X24400103","volume":"32","author":"K Shah","year":"2024","unstructured":"Shah, K., Abdalla, B., Abdeljawad, T. & Alqudah, M. A. A fractal\u2013fractional order model to study multiple sclerosis: A chronic disease. Fractals 32(2), 2440010. https:\/\/doi.org\/10.1142\/S0218348X24400103 (2024).","journal-title":"Fractals"},{"issue":"2","key":"20191_CR40","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1140\/epjp\/s13360-024-04910-z","volume":"139","author":"A Abidemi","year":"2024","unstructured":"Abidemi, A. & Owolabi, K. M. Unravelling the dynamics of Lassa fever transmission with nosocomial infections via non-fractional and fractional mathematical models. Eur. Phys. J. Plus 139(2), 108. https:\/\/doi.org\/10.1140\/epjp\/s13360-024-04910-z (2024).","journal-title":"Eur. Phys. J. Plus"},{"key":"20191_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2022.127259","volume":"597","author":"A Abidemi","year":"2022","unstructured":"Abidemi, A., Owolabi, K. M. & Pindza, E. Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission. Phys. A 597, 127259. https:\/\/doi.org\/10.1016\/j.physa.2022.127259 (2022).","journal-title":"Phys. A"},{"key":"20191_CR42","doi-asserted-by":"publisher","DOI":"10.1016\/j.dajour.2022.100156","volume":"6","author":"S Shyamsunder","year":"2022","unstructured":"Shyamsunder, S. et al. A new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks. Decis. Anal. J. 6, 100156. https:\/\/doi.org\/10.1016\/j.dajour.2022.100156 (2022).","journal-title":"Decis. Anal. J."},{"key":"20191_CR43","doi-asserted-by":"publisher","first-page":"2259","DOI":"10.1007\/s40808-022-01624-y","volume":"9","author":"A Abidemi","year":"2022","unstructured":"Abidemi, A., Owolabi, K. M. & Pindza, E. Assessing the dynamics of Lassa fever with impact of environmental sanitation: Optimal control and cost-effectiveness analysis. Model. Earth Syst. Environ. 9, 2259\u20132284. https:\/\/doi.org\/10.1007\/s40808-022-01624-y (2022).","journal-title":"Model. Earth Syst. Environ."},{"issue":"4","key":"20191_CR44","doi-asserted-by":"publisher","first-page":"149","DOI":"10.3390\/fractalfract5040149","volume":"5","author":"KS Nisar","year":"2021","unstructured":"Nisar, K. S., Abboubakar, H. & Regonne, R. K. Fractional dynamics of typhoid fever transmission models with mass vaccination perspectives. Fract. Fract. 5(4), 149. https:\/\/doi.org\/10.3390\/fractalfract5040149 (2021).","journal-title":"Fract. Fract."},{"key":"20191_CR45","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2021.111129","volume":"150","author":"H Abboubakar","year":"2021","unstructured":"Abboubakar, H., Kombou, L. K., Koko, A. D., Fouda, H. P. E. & Kumar, A. Projections and fractional dynamics of the typhoid fever: A case study of Mbandjock in the Centre Region of Cameroon. Chaos Solitons Fract. 150, 111129. https:\/\/doi.org\/10.1016\/j.chaos.2021.111129 (2021).","journal-title":"Chaos Solitons Fract."},{"key":"20191_CR46","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.110283","volume":"141","author":"KN Nabi","year":"2020","unstructured":"Nabi, K. N., Abboubakar, H. & Kumar, P. Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives. Chaos Solitons Fract. 141, 110283. https:\/\/doi.org\/10.1016\/j.chaos.2020.110283 (2020).","journal-title":"Chaos Solitons Fract."},{"key":"20191_CR47","doi-asserted-by":"publisher","first-page":"29290","DOI":"10.1038\/s41598-025-14280-w","volume":"15","author":"BC Agbata","year":"2025","unstructured":"Agbata, B. C. et al. Fractional-order model of malaria incorporating treatment and prevention strategies. Sci. Rep. 15, 29290. https:\/\/doi.org\/10.1038\/s41598-025-14280-w (2025).","journal-title":"Sci. Rep."},{"key":"20191_CR48","doi-asserted-by":"publisher","unstructured":"Omeje, D., Acheneje, G., Odiba, P. & Bolarinwa, B. Modelling the transmission dynamics of the coinfection of Malaria and Tuberculosis with optimal control strategies cost effectiveness analysis. Res. Sq. Preprint. https:\/\/doi.org\/10.21203\/rs.3rs-5312505\/v1 (2024).","DOI":"10.21203\/rs.3rs-5312505\/v1"},{"issue":"6","key":"20191_CR49","doi-asserted-by":"publisher","DOI":"10.1002\/eng2.70210","volume":"7","author":"BC Agbata","year":"2025","unstructured":"Agbata, B. C. et al. Mathematical analysis of the transmission dynamics of malaria and tuberculosis co-infection with control strategies. Eng. Rep. 7(6), e70210. https:\/\/doi.org\/10.1002\/eng2.70210 (2025).","journal-title":"Eng. Rep."},{"issue":"1","key":"20191_CR50","doi-asserted-by":"publisher","first-page":"21","DOI":"10.59292\/bulletinbiomath.2024002","volume":"2","author":"B Bolarinwa","year":"2024","unstructured":"Bolarinwa, B., Onoja, T., Agbata, B. C., Omede, B. I. & Odionyenma, U. B. Dynamical analysis of HIV-TB coinfection in the presence of treatment for TB. Bull. Biomath. 2(1), 21\u201356. https:\/\/doi.org\/10.59292\/bulletinbiomath.2024002 (2024).","journal-title":"Bull. Biomath."},{"issue":"4","key":"20191_CR51","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/BF00178324","volume":"28","author":"O Diekmann","year":"1990","unstructured":"Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. J. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28(4), 365\u2013382. https:\/\/doi.org\/10.1007\/BF00178324 (1990).","journal-title":"J. Math. Biol."},{"key":"20191_CR52","doi-asserted-by":"publisher","DOI":"10.1186\/s12992-020-00621-x","volume":"16","author":"FA M\u00e9ndez","year":"2020","unstructured":"M\u00e9ndez, F. A. & Trussell, J. W. Healthcare access and malaria control: Evaluating the effectiveness of interventions in low-income settings. Glob. Health. 16, 103. https:\/\/doi.org\/10.1186\/s12992-020-00621-x (2020).","journal-title":"Glob. Health."},{"key":"20191_CR53","doi-asserted-by":"publisher","DOI":"10.1186\/1475-2875-13-428","volume":"13","author":"LC Okell","year":"2014","unstructured":"Okell, L. C., Drakeley, C. J., Ghani, A. C., Bousema, T. & Sutherland, C. J. Reduction of transmission from malaria patients by artemisinin combination therapies: A pooled analysis of six randomized trials. Malar. J. 13, 428. https:\/\/doi.org\/10.1186\/1475-2875-13-428 (2014).","journal-title":"Malar. J."},{"issue":"4","key":"20191_CR54","doi-asserted-by":"publisher","first-page":"1675","DOI":"10.55214\/25768484.v9i4.6353","volume":"9","author":"CB Agbata","year":"2025","unstructured":"Agbata, C. B., Meco, Z. M., Agbebaku, D. F., Dervishi, R. & Ezike, M. G. C. Fractional-order analysis of malaria and tuberculosis co-dynamics: A Laplace Adomian decomposition approach. Edelweiss Appl. Sci. Technol. 9(4), 1675\u20131714. https:\/\/doi.org\/10.55214\/25768484.v9i4.6353 (2025).","journal-title":"Edelweiss Appl. Sci. Technol."},{"key":"20191_CR55","doi-asserted-by":"publisher","DOI":"10.1186\/s12879-025-10653-8","volume":"25","author":"E Akowe","year":"2025","unstructured":"Akowe, E. et al. A novel malaria mathematical model: Integrating vector and non-vector transmission pathways. BMC Infect. Dis. 25, 322. https:\/\/doi.org\/10.1186\/s12879-025-10653-8 (2025).","journal-title":"BMC Infect. Dis."},{"issue":"403","key":"20191_CR56","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-021-03494-7","volume":"2021","author":"A Atangana","year":"2021","unstructured":"Atangana, A. Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?. Adv. Differ. Equ. 2021(403), 403. https:\/\/doi.org\/10.1186\/s13662-021-03494-7 (2021).","journal-title":"Adv. Differ. Equ."},{"key":"20191_CR57","unstructured":"World Health Organization. World malaria report https:\/\/www.who.int\/publications\/i\/item\/9789240068487 (World Health Organization, 2023)."},{"issue":"2","key":"20191_CR58","first-page":"59","volume":"21","author":"BC Agbata","year":"2023","unstructured":"Agbata, B. C. et al. A mathematical model of COVID-19 transmission dynamics with effects of awareness and vaccination program. J. Ghana Sci. Assoc. 21(2), 59\u201361 (2023).","journal-title":"J. Ghana Sci. Assoc."},{"issue":"1","key":"20191_CR59","doi-asserted-by":"publisher","first-page":"10","DOI":"10.21010\/ajid.v15i1.2","volume":"15","author":"QO Ahman","year":"2021","unstructured":"Ahman, Q. O., Omale, D., Asogwa, C. C., Nnaji, D. U. & Mbah, G. C. E. Transmission dynamics of Ebola Virus Disease with vaccine, condom use, quarantine, isolation, and treatment drug. Afr. J. Infect. Dis. 15(1), 10\u201323 (2021).","journal-title":"Afr. J. Infect. Dis."},{"issue":"1\u20132","key":"20191_CR60","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P Vanden Driessche","year":"2002","unstructured":"Vanden Driessche, P. & Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1\u20132), 29\u201348 (2002).","journal-title":"Math. Biosci."},{"issue":"1","key":"20191_CR61","doi-asserted-by":"publisher","first-page":"10","DOI":"10.21010\/Ajidv17i1.2","volume":"17","author":"GCE Mbah","year":"2023","unstructured":"Mbah, G. C. E. et al. Mathematical modelling approach of the study of Ebola Virus Disease transmission dynamics in a developing country. Afr. J. Infect. Dis. 17(1), 10\u201326. https:\/\/doi.org\/10.21010\/Ajidv17i1.2 (2023).","journal-title":"Afr. J. Infect. Dis."},{"issue":"6","key":"20191_CR62","doi-asserted-by":"publisher","first-page":"1789","DOI":"10.2298\/FIL2206789A","volume":"36","author":"AK Alzahrani","year":"2022","unstructured":"Alzahrani, A. K. & Khan, M. A. The co-dynamics of malaria and Tuberculosis with optimal control strategies. Filomat 36(6), 1789\u20131818. https:\/\/doi.org\/10.2298\/FIL2206789A (2022).","journal-title":"Filomat"},{"issue":"1","key":"20191_CR63","first-page":"1","volume":"7","author":"JO Odeh","year":"2024","unstructured":"Odeh, J. O. et al. A mathematical model for the control of chlamydia disease with treatment strategy. J. Math. Acumen Res. 7(1), 1\u201320 (2024).","journal-title":"J. Math. Acumen Res."},{"issue":"3B","key":"20191_CR64","doi-asserted-by":"publisher","first-page":"202","DOI":"10.4314\/dujopas.v10i3b.19","volume":"10","author":"BC Agbata","year":"2024","unstructured":"Agbata, B. C. et al. Numerical solution of fractional order model of measles disease with double dose vaccination. DUJOPAS 10(3B), 202\u2013217. https:\/\/doi.org\/10.4314\/dujopas.v10i3b.19 (2024).","journal-title":"DUJOPAS"},{"issue":"3","key":"20191_CR65","doi-asserted-by":"publisher","first-page":"17","DOI":"10.37745\/ijmss.13\/vol12n31751","volume":"12","author":"GO Acheneje","year":"2024","unstructured":"Acheneje, G. O. et al. Approximate solution of the fractional order mathematical model on the transmission dynamics of the co-infection of COVID-19 and Monkeypox using the Laplace-Adomian decomposition method. Int. J. Math. Stat. Stud. 12(3), 17\u201351 (2024).","journal-title":"Int. J. Math. Stat. Stud."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-025-20191-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-025-20191-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-025-20191-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:46:08Z","timestamp":1760712368000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-025-20191-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,17]]},"references-count":65,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["20191"],"URL":"https:\/\/doi.org\/10.1038\/s41598-025-20191-7","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,17]]},"assertion":[{"value":"7 August 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"36359"}}