{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,18]],"date-time":"2026-10-18T18:29:05Z","timestamp":1792348145803,"version":"4.4.0"},"reference-count":65,"publisher":"The Royal Society","issue":"242","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["DP240102585"],"award-info":[{"award-number":["DP240102585"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Vaccines not only directly protect vaccinated individuals but also contribute to protecting the entire population via indirect herd-immunity benefits. However, researchers have long struggled to quantify these indirect effects at the population level, hindering the assessment of vaccination programme effectiveness. We developed a new method to estimate these effects, thereby markedly improving measures of the number of infections, hospitalizations and deaths averted by vaccination. Our population-based analysis of 6\u202f440\u202f000 residents of Victoria, Australia, reveals strong indirect effects during the Delta outbreak (September\u2013November 2021). By modelling a non-vaccination counterfactual, we conservatively estimate 315\u202f000 infections were averted (95% Bayesian credible interval (BCI): 231k\u2013406k), as well as 33\u202f400 hospitalizations (95% BCI: 22k\u201346k), and 4900 deaths (95% BCI: 2.8k\u20137.2k). These are 4.0, 7.5 and 8.0 times higher, respectively, than observed. Half of the averted infections and around one-quarter of hospitalizations and deaths were attributable to indirect protection. Homogeneous vaccination across local government areas could have reduced outcomes by approximately 25%.<\/jats:p>","DOI":"10.1098\/rsif.2025.0839","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T05:37:13Z","timestamp":1790746633000},"source":"Crossref","is-referenced-by-count":1,"title":["Quantifying the direct and indirect impact of COVID-19 vaccination: evidence from Victoria, Australia"],"prefix":"10.1098","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8339-5965","authenticated-orcid":false,"given":"Lixin","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Mathematical and Geospatial Sciences, School of Science, RMIT University 1 , Melbourne, Victoria, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haydar","family":"Demirhan","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Geospatial Sciences, School of Science, RMIT University 1 , Melbourne, Victoria, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Eizenberg","sequence":"additional","affiliation":[{"name":"Doctors of Ivanhoe 3 , Melbourne, Victoria, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Trauer","sequence":"additional","affiliation":[{"name":"School of Public Health and Preventive Medicine, Monash University 4 , Melbourne, Victoria, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6465-579X","authenticated-orcid":false,"given":"Lewi","family":"Stone","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Science, RMIT University 2 , Melbourne, Victoria, Australia"},{"name":"Department of Biomathematics Unit, Faculty of Life Sciences, Tel Aviv University 5 , Tel Aviv-Yafo, Tel Aviv District, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2026,9,30]]},"reference":[{"key":"2026093001370546500_RSIF20250839C1","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1038\/s41577-021-00592-1","article-title":"Progress of the COVID-19 vaccine effort: viruses, vaccines and variants versus efficacy, effectiveness and escape","volume":"21","author":"Tregoning","year":"2021","journal-title":"Nat. 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