{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T22:11:13Z","timestamp":1775167873477,"version":"3.50.1"},"reference-count":30,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"The Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We investigate game-theory based decisions on vaccination uptake and its effects on the spread of an epidemic with nonlinear incidence rate. It is assumed that each individual\u2019s decision approximates his\/her best response (called smoothed best response) in that this person chooses to take the vaccine based on its cost-benefit analysis. The basic reproduction number of the resultant epidemic model is calculated and used to characterize the existence and stability of the disease-free and endemic equilibria of the model. The effects on the spread and control of the epidemic are revealed in terms of the sensitivity of the response to changes in costs and benefits, in the \u201ccost\u201d of the vaccination, and in the proportion of susceptible individuals who are faced with the decision of whether or not to be vaccinated per unit time. The effects of the best response decision rule are also analyzed and compared to those of the smoothed best response. Our study shows that, when there is a perceived cost to take the vaccine, the smoothed best response is more effective in controlling the epidemic. However, when this cost is 0, the best response is the more efficient control.<\/jats:p>","DOI":"10.1155\/2014\/825734","type":"journal-article","created":{"date-parts":[[2014,2,16]],"date-time":"2014-02-16T16:03:13Z","timestamp":1392566593000},"page":"1-14","source":"Crossref","is-referenced-by-count":13,"title":["Disease Control through Voluntary Vaccination Decisions Based on the Smoothed Best Response"],"prefix":"10.1155","volume":"2014","author":[{"given":"Fei","family":"Xu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3C5"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ross","family":"Cressman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3C5"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2008.02.026"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.vaccine.2009.04.079"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.tpb.2009.08.003"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1080\/17513758.2010.510213"},{"key":"5","year":"2000"},{"key":"6","year":"2003"},{"key":"7","year":"1998"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1890\/10-0199.1"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1086\/506970"},{"issue":"6","key":"10","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1093\/oxfordjournals.aje.a114471","volume":"124","year":"1986","journal-title":"American Journal of Epidemiology"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0403823101"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.2005.3153"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2006.08.015"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2334-9-77"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1000280"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2011.01.003"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.ecolmodel.2011.02.019"},{"issue":"4","key":"18","volume":"8","year":"2012","journal-title":"PLoS Computational Biology"},{"key":"19","doi-asserted-by":"crossref","first-page":"4807","DOI":"10.1016\/j.physa.2012.05.009","volume":"391","year":"2012","journal-title":"Physica A"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2012.04.003"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2012.03.002"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2011.11.005"},{"issue":"4","key":"23","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1137\/S0036144500371907","volume":"42","year":"2000","journal-title":"SIAM Review"},{"key":"24","first-page":"1","volume":"18","year":"1845","journal-title":"Nouveaux M\u00e9moires de l'Acad\u00e9mie Royale des Sciences et Belles-Lettres de Bruxelles"},{"key":"25","year":"2003"},{"key":"26"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(02)00108-6"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139902413829"},{"issue":"9-10","key":"29","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1016\/S0895-7177(02)00257-1","volume":"36","year":"2002","journal-title":"Mathematical and Computer Modelling"},{"key":"30","year":"1976"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2014\/825734.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2014\/825734.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2014\/825734.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T03:58:27Z","timestamp":1498103907000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/cmmm\/2014\/825734\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":30,"alternative-id":["825734","825734"],"URL":"https:\/\/doi.org\/10.1155\/2014\/825734","relation":{},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"value":"1748-670X","type":"print"},{"value":"1748-6718","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}