{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T14:59:07Z","timestamp":1781103547590,"version":"3.54.1"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T00:00:00Z","timestamp":1771545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100021171","name":"Guangdong Basic and Applied Basic Research Foundation","doi-asserted-by":"crossref","award":["2023A1515110305"],"award-info":[{"award-number":["2023A1515110305"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Guangdong Provincial Department of Education Youth Innovative Talents Project","award":["2023KQNCX087"],"award-info":[{"award-number":["2023KQNCX087"]}]},{"name":"Jiangmen Basic and Theoretical Science Research Technology Program Project","award":["2023JC01008"],"award-info":[{"award-number":["2023JC01008"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62503372"],"award-info":[{"award-number":["62503372"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Vaccination behavior and epidemic spreading are strongly intertwined processes, and their coevolution is often shaped by both individual decision-making and social interactions. However, most existing studies model such interactions at the pairwise level, overlooking the potential impact of higher-order social influence arising from group interactions. In this work, we develop a coupled vaccination\u2013epidemic spreading model on multilayer higher-order networks, where vaccination behavior evolves on a simplicial complex and epidemic propagation occurs on a physical contact network. The model incorporates imperfect vaccine efficacy, allowing vaccinated individuals to become infected, and introduces a hybrid vaccination strategy that combines rational cost\u2013benefit evaluation with social influence from both pairwise and higher-order interactions, as well as negative effects induced by vaccine failure. By constructing the coupled dynamical equations, we analytically derive the epidemic outbreak threshold and elucidate how higher-order interactions, behavioral responses, and vaccine-related parameters jointly affect epidemic dynamics. Numerical simulations on networks with different structural properties validate the theoretical results and reveal pronounced structure-dependent effects. The results show that higher-order social interactions can significantly reshape vaccination behavior and epidemic prevalence, while network heterogeneity and vaccine imperfection play crucial roles in determining the outbreak threshold and steady-state infection level. These results emphasize the necessity of incorporating higher-order interactions together with realistic vaccination behavior into epidemic modeling and offer new insights for the design of effective vaccination strategies.<\/jats:p>","DOI":"10.3390\/e28020243","type":"journal-article","created":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T08:50:03Z","timestamp":1771577403000},"page":"243","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Coupled Dynamics of Vaccination Behavior and Epidemic Spreading on Multilayer Higher-Order Networks"],"prefix":"10.3390","volume":"28","author":[{"given":"Zhishuang","family":"Wang","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Wuyi University, Jiangmen 529020, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-9722-6561","authenticated-orcid":false,"given":"Guoqiang","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Wuyi University, Jiangmen 529020, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qian","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Wuyi University, Jiangmen 529020, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linyuan","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Wuyi University, Jiangmen 529020, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5409-2962","authenticated-orcid":false,"given":"Zhiyong","family":"Hong","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Wuyi University, Jiangmen 529020, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1038\/s41579-021-00639-z","article-title":"Infectious disease in an era of global change","volume":"20","author":"Baker","year":"2022","journal-title":"Nat. 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