{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T17:20:22Z","timestamp":1785000022977,"version":"3.55.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T00:00:00Z","timestamp":1768262400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T00:00:00Z","timestamp":1770249600000},"content-version":"vor","delay-in-days":23,"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\/s41598-025-34872-w","type":"journal-article","created":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T19:55:54Z","timestamp":1768334154000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A generalized SEIRW-VN framework for modeling infectious disease dynamics"],"prefix":"10.1038","volume":"16","author":[{"given":"Abdoulaye","family":"Sow","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cherif","family":"Diallo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hocine","family":"Cherifi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,13]]},"reference":[{"key":"34872_CR1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0295025","author":"A Sow","year":"2024","unstructured":"Sow, A., Yong, B., Diallo, C. & Cherifi, H. Interplay between vaccines and treatment for dengue control: An epidemic model. PLOS One https:\/\/doi.org\/10.1371\/journal.pone.0295025 (2024).","journal-title":"PLOS One"},{"key":"34872_CR2","doi-asserted-by":"publisher","DOI":"10.1155\/2022\/5366395","author":"A Sow","year":"2022","unstructured":"Sow, A., Diallo, C., Cherifi, H. & Cheong, S. A. Effects of vertical transmission and human contact on Zika dynamics. Complexity https:\/\/doi.org\/10.1155\/2022\/5366395 (2022).","journal-title":"Complexity"},{"issue":"1","key":"34872_CR3","doi-asserted-by":"publisher","first-page":"3746855","DOI":"10.1155\/cplx\/3746855","volume":"2025","author":"Abdoulaye Sow","year":"2025","unstructured":"Sow, Abdoulaye, Diallo, Cherif & Cherifi, Hocine. Analysis of vaccination strategies and epidemic therapy in heterogeneous networks: The monkey pox case. Complexity 2025(1), 3746855 (2025).","journal-title":"Complexity"},{"key":"34872_CR4","doi-asserted-by":"crossref","unstructured":"Hoang, M. T., & Ehrhardt, M. Differential equation models for infectious diseases: Mathematical modeling, qualitative analysis, numerical methods and applications. SeMA J. (2025).","DOI":"10.1007\/s40324-025-00404-9"},{"key":"34872_CR5","first-page":"181","volume-title":"Infectious disease spreading modeling and containing strategy in heterogeneous population","author":"W Li","year":"2024","unstructured":"Li, W. et al. Infectious disease spreading modeling and containing strategy in heterogeneous population 181 (Chaos, 2024)."},{"key":"34872_CR6","doi-asserted-by":"crossref","unstructured":"Sandu, A. M. et al. Healthcare-associated infections: The role of microbial and environmental factors in infection control-a narrative review. Infectious Diseases Therapy 14, 933\u2013971 (2025).","DOI":"10.1007\/s40121-025-01143-0"},{"issue":"1","key":"34872_CR7","first-page":"1","volume":"1","author":"H Kakeya","year":"2025","unstructured":"Kakeya, H., Itoh, M., Kamijima, Y., Nitta, T. & Umeno, Y. Unreliability in simulations of COVID-19 cases and deaths based on transmission models. J. Math. Epidemiol. 1(1), 1\u201310 (2025).","journal-title":"J. Math. Epidemiol."},{"key":"34872_CR8","unstructured":"Lu, X., Feng, J., Lai, S., & Holme, P. Human mobility in epidemic modeling. arXiv preprintarXiv:2507.22799 (2025) ."},{"issue":"5","key":"34872_CR9","doi-asserted-by":"publisher","first-page":"507","DOI":"10.3390\/e27050507","volume":"27","author":"D Diallo","year":"2025","unstructured":"Diallo, D. et al. Integrating human mobility models with epidemic modeling: A framework for generating synthetic temporal contact networks. Entropy 27(5), 507 (2025).","journal-title":"Entropy"},{"key":"34872_CR10","doi-asserted-by":"crossref","unstructured":"Wang, M., Peng, L., Jia, B., & Hong, L. Epidemic dynamics in physical\u2013information\u2013social multilayer networks. arXiv preprint arXiv:2506.00104 (2025).","DOI":"10.2139\/ssrn.5297786"},{"key":"34872_CR11","doi-asserted-by":"crossref","unstructured":"Liu, S., Gong, S., Feng, T., Liu, Z., Lau, M. S. Y., & Jin, W. Higher-order Interaction Matters: Dynamic Hypergraph Neural Networks for Epidemic Modeling. arXiv preprint arXiv:2503.20114 (2025).","DOI":"10.1142\/9789819824755_0005"},{"key":"34872_CR12","doi-asserted-by":"crossref","unstructured":"Malizia, F., Guzm\u00e1n, A., Iacopini, I., & Kiss, I. Z. Disentangling the role of heterogeneity and hyperedge overlap in explosive contagion on higher-order networks. arXiv preprint arXiv:2501.17800 (2025).","DOI":"10.1103\/z3d5-94zb"},{"key":"34872_CR13","doi-asserted-by":"crossref","unstructured":"Fouad, A. A., & El Antably, A. Agent-based modeling and simulation of pandemic propagation in a school environment. SAGE Open (2023).","DOI":"10.1177\/14780771221089886"},{"key":"34872_CR14","doi-asserted-by":"publisher","first-page":"1394","DOI":"10.1186\/s12879-024-10245-y","volume":"24","author":"VL Bui","year":"2024","unstructured":"Bui, V. L. et al. Agent-based modelling of Mycobacterium tuberculosis transmission: A systematic review. BMC Infectious Diseases 24, 1394 (2024).","journal-title":"BMC Infectious Diseases"},{"key":"34872_CR15","doi-asserted-by":"crossref","unstructured":"Steinh\u00f6fel, K. K., Heslop, D., & MacIntyre, C. R. Agent-Based Models of Virus Infection. Curr. Clin. Microbiol. Rep., 12(2) (2025).","DOI":"10.1007\/s40588-024-00238-5"},{"key":"34872_CR16","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1186\/s12879-024-09330-z","volume":"24","author":"S Evans","year":"2024","unstructured":"Evans, S. et al. Impact of interventions to reduce nosocomial transmission of SARS-CoV-2 in English NHS Trusts: A computational modelling study. BMC Infect. Diseases 24, 475 (2024).","journal-title":"BMC Infect. Diseases"},{"key":"34872_CR17","doi-asserted-by":"publisher","first-page":"1371","DOI":"10.1186\/s12879-024-10243-0","volume":"24","author":"M Shankar","year":"2024","unstructured":"Shankar, M. et al. How mathematical modelling can inform outbreak response vaccination. BMC Infect. Diseases24, 1371 (2024).","journal-title":"BMC Infect. Diseases"},{"key":"34872_CR18","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1140\/epjp\/s13360-025-06123-4","volume":"140","author":"CE Madubueze","year":"2025","unstructured":"Madubueze, C. E., Ajao, S., Akanni, J. O., Fatmawati, F. & Chazuka, Z. Impact of environmental contamination on Lassa fever transmission dynamics: A mathematical modelling approach. Eur. Phys. J. Plus 140, 202 (2025).","journal-title":"Eur. Phys. J. Plus"},{"key":"34872_CR19","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1007\/s11538-023-01235-3","volume":"86","author":"IZ Kiss","year":"2024","unstructured":"Kiss, I. Z., Berthouze, L. & KhudaBukhsh, W. R. Towards inferring network properties from epidemic data. Bull. Math. Biol. 86, 6 (2024).","journal-title":"Bull. Math. Biol."},{"issue":"2","key":"34872_CR20","doi-asserted-by":"publisher","first-page":"324","DOI":"10.3934\/mbe.2025013","volume":"22","author":"MB Hridoy","year":"2025","unstructured":"Hridoy, M. B. An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models. Math. Biosci. Eng. 22(2), 324\u2013354 (2025).","journal-title":"Math. Biosci. Eng."},{"key":"34872_CR21","doi-asserted-by":"crossref","unstructured":"Mossong, J. et al. Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS medicine 5(3), e74 (2008).","DOI":"10.1371\/journal.pmed.0050074"},{"issue":"16","key":"34872_CR22","doi-asserted-by":"publisher","first-page":"1564","DOI":"10.1056\/NEJMc2004973","volume":"382","author":"N van Doremalen","year":"2020","unstructured":"van Doremalen, N. et al. Aerosol and surface stability of SARS-CoV-2 as compared with SARS-CoV-1. New England J. Med. 382(16), 1564\u20131567 (2020).","journal-title":"New England J. Med."},{"key":"34872_CR23","doi-asserted-by":"crossref","unstructured":"of the People, National Health Commission. Protocol for prevention and control of COVID-19 (edition 6).\u201d China CDC Weekly 2.19 (2020): 321.","DOI":"10.46234\/ccdcw2020.082"},{"key":"34872_CR24","doi-asserted-by":"crossref","unstructured":"Luo, X., Feng, S., Yang, J., Peng, X. L., Cao, X., Zhang, J., & Jin, Z. Analysis of potential risk of COVID-19 infections in China based on a pairwise epidemic model (2020).","DOI":"10.20944\/preprints202002.0398.v1"},{"issue":"1","key":"34872_CR25","doi-asserted-by":"publisher","first-page":"142","DOI":"10.3390\/math11010142","volume":"11","author":"IU Haq","year":"2022","unstructured":"Haq, I. U., Ullah, N., Ali, N. & Nisar, K. S. A new mathematical model of COVID-19 with quarantine and vaccination. Mathematics 11(1), 142 (2022).","journal-title":"Mathematics"},{"issue":"5","key":"34872_CR26","doi-asserted-by":"publisher","first-page":"467","DOI":"10.3390\/vaccines9050467","volume":"9","author":"A Pormohammad","year":"2021","unstructured":"Pormohammad, A. et al. Efficacy and safety of COVID-19 vaccines: A systematic review and meta-analysis of randomized clinical trials. Vaccines 9(5), 467 (2021).","journal-title":"Vaccines"},{"key":"34872_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2020.103642","volume":"19","author":"CT Deressa","year":"2020","unstructured":"Deressa, C. T., Mussa, Y. O. & Duressa, G. F. Optimal control and sensitivity analysis for transmission dynamics of Coronavirus. Results Phys. 19, 103642 (2020).","journal-title":"Results Phys."},{"key":"34872_CR28","unstructured":"European Centre for Disease Prevention and Control (ECDC). Coronavirus disease 2019 (COVID-19) in the EU\/EEA and the UK \u2013 daily aggregated data, https:\/\/www.ecdc.europa.eu\/en\/publications-data\/download-todays-data-geographic-distribution-covid-19-cases-worldwide, accessed 2020."},{"issue":"6","key":"34872_CR29","doi-asserted-by":"publisher","first-page":"2777","DOI":"10.1007\/s00180-013-0428-3","volume":"28","author":"M Lenormand","year":"2013","unstructured":"Lenormand, M., Jabot, F. & Deffuant, G. Adaptive approximate Bayesian computation for complex models. Comput. Statist. 28(6), 2777\u20132796 (2013).","journal-title":"Comput. Statist."},{"issue":"3","key":"34872_CR30","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1103\/RevModPhys.87.925","volume":"87","author":"R Pastor-Satorras","year":"2015","unstructured":"Pastor-Satorras, R., Castellano, C., Van Mieghem, P. & Vespignani, A. Epidemic processes in complex networks. Rev. Modern Phys. 87(3), 925\u2013979 (2015).","journal-title":"Rev. Modern Phys."},{"key":"34872_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-50806-1","volume-title":"Mathematics of Epidemics on Networks","author":"IZ Kiss","year":"2017","unstructured":"Kiss, I. Z., Miller, J. C. & Simon, P. L. Mathematics of Epidemics on Networks (Springer, 2017)."},{"key":"34872_CR32","doi-asserted-by":"publisher","first-page":"67","DOI":"10.12688\/wellcomeopenres.15842.3","volume":"5","author":"A Endo","year":"2020","unstructured":"Endo, A., Abbott, S., Kucharski, A. J. & Funk, S. Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China. Wellcome Open Res 5, 67 (2020).","journal-title":"Wellcome Open Res"},{"issue":"7066","key":"34872_CR33","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1038\/nature04153","volume":"438","author":"JO Lloyd-Smith","year":"2005","unstructured":"Lloyd-Smith, J. O., Schreiber, S. J., Kopp, P. E. & Getz, W. M. Superspreading and the effect of individual variation on disease emergence. Nature 438(7066), 355\u2013359 (2005).","journal-title":"Nature"},{"key":"34872_CR34","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1038\/s41591-020-0883-7","volume":"26","author":"G Giordano","year":"2020","unstructured":"Giordano, G. et al. Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. Nat. Med. 26, 855\u2013860 (2020).","journal-title":"Nat. Med."},{"issue":"1","key":"34872_CR35","doi-asserted-by":"publisher","first-page":"3449","DOI":"10.1038\/s41467-021-23761-1","volume":"12","author":"L Matrajt","year":"2021","unstructured":"Matrajt, L. et al. Optimizing vaccine allocation for COVID-19 vaccines shows the potential role of single-dose vaccination. Nat. Commun. 12(1), 3449 (2021).","journal-title":"Nat. Commun."},{"issue":"6516","key":"34872_CR36","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1126\/science.abe5960","volume":"370","author":"J Shaman","year":"2020","unstructured":"Shaman, J. & Galanti, M. Will SARS-CoV-2 become endemic?. Science 370(6516), 527\u2013529 (2020).","journal-title":"Science"},{"issue":"3","key":"34872_CR37","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1093\/comnet\/cnu016","volume":"2","author":"M Kivel\u00e4","year":"2014","unstructured":"Kivel\u00e4, M. et al. Multilayer networks. J. Complex Netw. 2(3), 203\u2013271 (2014).","journal-title":"J. Complex Netw."},{"issue":"9","key":"34872_CR38","first-page":"667","volume":"8","author":"S Funk","year":"2010","unstructured":"Funk, S., Salath\u00e9, M. & Jansen, V. A. A. Modelling the influence of human behaviour on the spread of infectious diseases. Nat. Rev. Microbiol. 8(9), 667\u2013673 (2010).","journal-title":"Nat. Rev. Microbiol."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-025-34872-w","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-025-34872-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-025-34872-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T10:52:56Z","timestamp":1770288776000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-025-34872-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,13]]},"references-count":38,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["34872"],"URL":"https:\/\/doi.org\/10.1038\/s41598-025-34872-w","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,13]]},"assertion":[{"value":"19 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 January 2026","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":"5137"}}