{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T13:33:40Z","timestamp":1775223220014,"version":"3.50.1"},"reference-count":30,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[2006,8,1]],"date-time":"2006-08-01T00:00:00Z","timestamp":1154390400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Theoretical Biology"],"published-print":{"date-parts":[[2006,8]]},"DOI":"10.1016\/j.jtbi.2006.01.012","type":"journal-article","created":{"date-parts":[[2006,3,1]],"date-time":"2006-03-01T19:20:38Z","timestamp":1141240838000},"page":"964-967","source":"Crossref","is-referenced-by-count":13,"title":["The earliest notes on the reproduction number in relation to herd immunity: Theophil Lotz and smallpox vaccination"],"prefix":"10.1016","volume":"241","author":[{"given":"Hiroshi","family":"Nishiura","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Klaus","family":"Dietz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Eichner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.jtbi.2006.01.012_bib1","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1126\/science.7063839","article-title":"Directly transmitted infectious diseases: control by vaccination","volume":"215","author":"Anderson","year":"1982","journal-title":"Science"},{"key":"10.1016\/j.jtbi.2006.01.012_bib2","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/0140-6736(90)90420-A","article-title":"Immunisation and herd immunity","volume":"335","author":"Anderson","year":"1990","journal-title":"Lancet"},{"key":"10.1016\/j.jtbi.2006.01.012_bib3","series-title":"Infectious Diseases of Humans: Dynamics and Control","author":"Anderson","year":"1991"},{"key":"10.1016\/j.jtbi.2006.01.012_bib4","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1017\/S0022172400066249","article-title":"Impact of population density on immunization programmes","volume":"96","author":"Arita","year":"1986","journal-title":"J. Hyg. (Lond)"},{"key":"10.1016\/j.jtbi.2006.01.012_bib5","series-title":"The Mathematical Theory of Infectious Diseases and its Applications","author":"Bailey","year":"1975"},{"key":"10.1016\/j.jtbi.2006.01.012_bib6","doi-asserted-by":"crossref","first-page":"10564","DOI":"10.1073\/pnas.1731324100","article-title":"Group interest versus self-interest in smallpox vaccination policy","volume":"100","author":"Bauch","year":"2003","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"10.1016\/j.jtbi.2006.01.012_bib7","series-title":"Statistisches Jahrbuch der Stadt Berlin, Zw\u00f6lfter Jahrgang. Statistik des Jahres 1884","author":"B\u00f6ckh","year":"1886"},{"key":"10.1016\/j.jtbi.2006.01.012_bib8","series-title":"Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation","author":"Diekmann","year":"2000"},{"key":"10.1016\/j.jtbi.2006.01.012_bib9","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1111\/j.1467-842X.1988.tb00464.x","article-title":"The first epidemic model: a historical note on P.D. En\u2019ko","volume":"30A","author":"Dietz","year":"1988","journal-title":"Aust. J. Stat."},{"key":"10.1016\/j.jtbi.2006.01.012_bib10","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1177\/096228029300200103","article-title":"The estimation of the basic reproduction number for infectious diseases","volume":"2","author":"Dietz","year":"1993","journal-title":"Stat. Methods Med. Res."},{"key":"10.1016\/j.jtbi.2006.01.012_bib11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0025-5564(02)00122-0","article-title":"Daniel Bernoulli's epidemiological model revisited","volume":"180","author":"Dietz","year":"2002","journal-title":"Math. Biosci."},{"key":"10.1016\/j.jtbi.2006.01.012_bib12","series-title":"Vaccination and small-pox in England and other countries: showing that compulsory re-vaccination is necessary with an account of the German Vaccination Commission of 1884, and extracts from the reports of the Royal Commission on Vaccination (1889), etc","author":"Edwardes","year":"1892"},{"key":"10.1016\/j.jtbi.2006.01.012_bib13","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1093\/aje\/kwg104","article-title":"Case isolation and contact tracing can prevent the spread of smallpox","volume":"158","author":"Eichner","year":"2003","journal-title":"Am. J. Epidemiol."},{"key":"10.1016\/j.jtbi.2006.01.012_bib14","series-title":"On the Course of Epidemics of Some Infectious Diseases","author":"En\u2019ko","year":"1889"},{"key":"10.1016\/j.jtbi.2006.01.012_bib15","series-title":"Annual report of the Registrar-General of Births, Deaths, and Marriages in England","article-title":"Second Report","author":"Farr","year":"1839"},{"key":"10.1016\/j.jtbi.2006.01.012_bib16","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1098\/rstl.1880.0009","article-title":"English reproduction table","volume":"I","author":"Farr","year":"1880","journal-title":"Philos Trans"},{"key":"10.1016\/j.jtbi.2006.01.012_bib17","series-title":"Smallpox and its Eradication","author":"Fenner","year":"1988"},{"key":"10.1016\/j.jtbi.2006.01.012_bib18","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1093\/oxfordjournals.epirev.a036121","article-title":"Herd immunity: history, theory, practice","volume":"15","author":"Fine","year":"1993","journal-title":"Epidemiol. Rev."},{"key":"10.1016\/j.jtbi.2006.01.012_bib19","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1093\/aje\/kwg251","article-title":"The interval between successive cases of an infectious disease","volume":"158","author":"Fine","year":"2003","journal-title":"Am. J. Epidemiol."},{"key":"10.1016\/j.jtbi.2006.01.012_bib20","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1093\/oxfordjournals.aje.a121310","article-title":"Herd immunity: basic concept and relevance to public health immunization practices","volume":"94","author":"Fox","year":"1971","journal-title":"Am. J. Epidemiol."},{"key":"10.1016\/j.jtbi.2006.01.012_bib21","doi-asserted-by":"crossref","first-page":"2101","DOI":"10.1002\/(SICI)1097-0258(19990830)18:16<2101::AID-SIM178>3.0.CO;2-6","article-title":"Estimation of the direct and indirect effects of vaccination","volume":"18","author":"Haber","year":"1999","journal-title":"Stat. Med."},{"key":"10.1016\/j.jtbi.2006.01.012_bib22","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1023\/A:1016599411804","article-title":"A brief history of R0 and a recipe for its calculation","volume":"50","author":"Heesterbeek","year":"2002","journal-title":"Acta. Biotheor."},{"key":"10.1016\/j.jtbi.2006.01.012_bib23","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1093\/shm\/11.1.49","article-title":"Vaccination policy against smallpox, 1835\u20131914: a comparison of England with Prussia and Imperial Germany","volume":"11","author":"Hennock","year":"1998","journal-title":"Soc. Hist. Med."},{"key":"10.1016\/j.jtbi.2006.01.012_bib24","unstructured":"Leichenrede, 1908. Zur Erinnerung an Herrn Theophil Lotz=Landerer, Dr. med. : geb. d. 28. October 1842, gest. d. 25 October 1908. Basel Staatsarchiv, Basel (in German)."},{"key":"10.1016\/j.jtbi.2006.01.012_bib25","doi-asserted-by":"crossref","first-page":"321","DOI":"10.2307\/2174080","article-title":"A note on the origin of the net reproduction ratio","volume":"38","author":"Lewes","year":"1984","journal-title":"Popul. Stud."},{"key":"10.1016\/j.jtbi.2006.01.012_bib26","series-title":"Pocken und vaccination. Bericht \u00fcber die Impffrage, erstattet im Namen der schweizerischen Sanit\u00e4tskommission an den schweizerischen Bundersrath","author":"Lotz","year":"1880"},{"key":"10.1016\/j.jtbi.2006.01.012_bib27","first-page":"813","article-title":"The analysis of equilibrium in malaria","volume":"49","author":"Macdonald","year":"1952","journal-title":"Trop. Dis. Bull."},{"key":"10.1016\/j.jtbi.2006.01.012_bib28","series-title":"The Prevention of Malaria","author":"Ross","year":"1911"},{"key":"10.1016\/j.jtbi.2006.01.012_bib29","series-title":"Public Health Reports. Sanitary Institute of Great Britain","author":"Simon","year":"1887"},{"key":"10.1016\/j.jtbi.2006.01.012_bib30","series-title":"F\u00fcr und wider die Kuhpockenimfung und den Impfzwang: oder, Polemische, kritische und statistische Beitr\u00e4ge zur Pocken- und Impffrage\/den schweiz","author":"Vogt","year":"1879"}],"container-title":["Journal of Theoretical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0022519306000257?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0022519306000257?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T04:06:15Z","timestamp":1555473975000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0022519306000257"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,8]]}},"alternative-id":["S0022519306000257"],"URL":"https:\/\/doi.org\/10.1016\/j.jtbi.2006.01.012","relation":{},"ISSN":["0022-5193"],"issn-type":[{"value":"0022-5193","type":"print"}],"subject":[],"published":{"date-parts":[[2006,8]]}}}