{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T09:37:07Z","timestamp":1788255427073,"version":"build-2803163510"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2011,3,16]],"date-time":"2011-03-16T00:00:00Z","timestamp":1300233600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2011,3,16]],"date-time":"2011-03-16T00:00:00Z","timestamp":1300233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bull Math Biol"],"published-print":{"date-parts":[[2011,11]]},"DOI":"10.1007\/s11538-011-9646-4","type":"journal-article","created":{"date-parts":[[2011,3,15]],"date-time":"2011-03-15T21:12:03Z","timestamp":1300223523000},"page":"2748-2772","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Impact of Imitation Processes on the Effectiveness of\u00a0Ring Vaccination"],"prefix":"10.1007","volume":"73","author":[{"given":"Chad R.","family":"Wells","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean M.","family":"Tchuenche","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lauren Ancel","family":"Meyers","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alison P.","family":"Galvani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chris T.","family":"Bauch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2011,3,16]]},"reference":[{"key":"9646_CR1","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.mbs.2005.06.005","volume":"198","author":"C. T. Bauch","year":"2005","unstructured":"Bauch, C. T. (2005). The spread of infectious diseases in a spatially structured population: an invasory pair approximation. Math. Biosci., 198, 217\u2013237.","journal-title":"Math. Biosci."},{"key":"9646_CR2","doi-asserted-by":"publisher","first-page":"13391","DOI":"10.1073\/pnas.0403823101","volume":"101","author":"C.T. Bauch","year":"2004","unstructured":"Bauch, C.T., & Earn, D.J.D. (2004). Vaccination and theory of games. Proc. Natl. Acad. Sci. USA, 101, 13391\u201313394.","journal-title":"Proc. Natl. Acad. Sci. USA"},{"issue":"Suppl. 3","key":"9646_CR3","first-page":"S120","volume":"17","author":"P. Bonanni","year":"1998","unstructured":"Bonanni, P. (1998). Demographic impact of vaccination: a review. Vaccine, 17(Suppl. 3), S120\u2013S125.","journal-title":"Vaccine"},{"key":"9646_CR4","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/0047-2727(91)90048-7","volume":"45","author":"D.L. Brito","year":"1991","unstructured":"Brito, D.L., Sheshinski, E., & Intriligator, M.D. (1991). Externalities and compulsory vaccinations. J.\u00a0Public Econ., 45, 69\u201390.","journal-title":"J.\u00a0Public Econ."},{"key":"9646_CR5","unstructured":"Chane, F.H., & Cottrell, A. (2009). Dynamic Equilibria in an Epidemic Model with voluntary vaccination. J. Biol. Dyn."},{"key":"9646_CR6","doi-asserted-by":"publisher","first-page":"1486","DOI":"10.1542\/peds.2005-1381","volume":"117","author":"A. F. Dempsey","year":"2006","unstructured":"Dempsey, A. F., Zimet, G. D., Davis, R. L., & Koutsky, L. (2006). Factors that are associated with parental acceptance of human papillomavirus vaccines: a randomized intervention study of written information about HPV. Pediatrics, 117, 1486\u20131493.","journal-title":"Pediatrics"},{"issue":"3","key":"9646_CR7","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/s101980100069","volume":"2","author":"R. Diel","year":"2000","unstructured":"Diel, R., Rappenhoener, B., & Schneider, S. (2000). Cost-effectiveness of hepatitis A immunization of children and adolescents in Germany. Eur. J. Health Econ., 2(3), 96\u2013103.","journal-title":"Eur. J. Health Econ."},{"key":"9646_CR8","volume-title":"Smallpox and its eradication","author":"F. D. A. Fenner","year":"1988","unstructured":"Fenner, F. D. A., Henderon, D. A., Arita, I., Jezek, Z., & Ladnyi, I. D. (1988). Smallpox and its eradication. Geneva: World Health Organization."},{"key":"9646_CR9","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1038\/nature04017","volume":"437","author":"N. M. Ferguson","year":"2005","unstructured":"Ferguson, N. M., Cummings, D. A. T., Cauchemez, S., Fraser, C., Riley, S., et al. (2005). Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature, 437, 209\u2013214.","journal-title":"Nature"},{"key":"9646_CR10","doi-asserted-by":"publisher","first-page":"6872","DOI":"10.1073\/pnas.0810762106","volume":"106","author":"S. Funk","year":"2009","unstructured":"Funk, S., Gilad, E., Watkins, C., & Jasen, V.A.A. (2009). The spread of awareness and its impact on epidemic outbreaks. Proc. Natl. Acad. Sci. USA, 106, 6872\u20136887.","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"9646_CR11","doi-asserted-by":"publisher","first-page":"5692","DOI":"10.1073\/pnas.0606774104","volume":"104","author":"A. Galvani","year":"2007","unstructured":"Galvani, A., Reluga, T., & Chapman, G. (2007). Longstanding influenza vaccination policy is in accord with individual self interest but not with the utilitarian optimum. Proc. Natl. Acad. Sci. USA, 104, 5692\u20135697.","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"9646_CR12","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1080\/15326348608807041","volume":"2","author":"D. Greenhalgh","year":"1986","unstructured":"Greenhalgh, D. (1986). Optimal control of an epidemic by ring vaccination. Commun. Stat., Stoch. Models, 2, 339\u2013363.","journal-title":"Commun. Stat., Stoch. Models"},{"issue":"3","key":"9646_CR13","first-page":"321","volume":"22","author":"J. W. Hopkins","year":"1988","unstructured":"Hopkins, J. W. (1988). The eradication of smallpox: organizational learning and innovation in international health administration. J. Dev. Areas, 22(3), 321\u201332.","journal-title":"J. Dev. Areas"},{"issue":"3","key":"9646_CR14","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1097\/01.ede.0000121821.02642.a4","volume":"15","author":"E. Kaplan","year":"2004","unstructured":"Kaplan, E. (2004). Preventing second-generation infections in a smallpox bioterrorist attack. Epidemiology, 15(3), 264\u2013270.","journal-title":"Epidemiology"},{"key":"9646_CR15","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1098\/rspb.1999.0716","volume":"266","author":"M. J. Keeling","year":"1999","unstructured":"Keeling, M. J. (1999). The effects of local spatial structure on epidemiology invasions. Proc. R. Soc. Lond. B, 266, 859\u2013867.","journal-title":"Proc. R. Soc. Lond. B"},{"key":"9646_CR16","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1038\/nature01343","volume":"421","author":"M. J. Keeling","year":"2003","unstructured":"Keeling, M. J., Woolhouse, M. E. J., May, R. M., Davies, G., & Grenfell, B. T. (2003). Modelling vaccination strategies against foot-and-mouth disease. Nature, 421, 136\u2013142.","journal-title":"Nature"},{"key":"9646_CR17","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1017\/S1355770X0700383X","volume":"12","author":"E. Klein","year":"2007","unstructured":"Klein, E., Laxminarayan, R., Smith, D., & Gilligan, C. (2007). Economic incentive and mathematical models of disease. Environ. Dev. Econ., 12, 707\u2013732.","journal-title":"Environ. Dev. Econ."},{"issue":"5","key":"9646_CR18","doi-asserted-by":"crossref","first-page":"832","DOI":"10.3201\/eid1005.030419","volume":"10","author":"M. Kretzschmar","year":"2004","unstructured":"Kretzschmar, M., van\u00a0den Hof, S., Wallinga, J., & van Wijngaarden, J. (2004). Ring vaccination and smallpox control. Emerg. Infect. Dis., 10(5), 832\u2013841.","journal-title":"Emerg. Infect. Dis."},{"key":"9646_CR19","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1038\/nature04153","volume":"438","author":"J. O. Lloyd-Smith","year":"2005","unstructured":"Lloyd-Smith, J. O., Schreiber, S. J., Kopp, P. E., & Getz, W. M. (2005). Superspreading and the effect of individual variation on disease emergence. Nature, 438, 355\u2013359.","journal-title":"Nature"},{"key":"9646_CR20","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.jtbi.2004.07.026","volume":"232","author":"L. A. Meyers","year":"2005","unstructured":"Meyers, L. A., Pourbohloul, B., Newman, M. E. J., Skowronski, D. M., & Brunham, R. C. (2005). Network theory and SARS: predicting outbreak diversity. J. Theor. Biol., 232, 71\u201381.","journal-title":"J. Theor. Biol."},{"key":"9646_CR21","doi-asserted-by":"publisher","first-page":"146","DOI":"10.2105\/AJPH.48.2.146","volume":"48","author":"M. Merrill","year":"1958","unstructured":"Merrill, M., Hollister, A., Gibbens, S., et al. (1958). Attitudes of Californians toward poliomyelitis vaccination. Am. J. Publ. Health, 48, 146\u2013152.","journal-title":"Am. J. Publ. Health"},{"key":"9646_CR22","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0001839","volume":"3","author":"S. Moghadas","year":"2008","unstructured":"Moghadas, S., Bowman, C., R\u00f6st, G., et al. (2008). Population-wide emergence of antiviral resistance during pandemic influenza. PLoS ONE, 3, e1839.","journal-title":"PLoS ONE"},{"key":"9646_CR23","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/s002850070003","volume":"41","author":"J. Muller","year":"2000","unstructured":"Muller, J., Schonfisch, B., & Kirkilionis, M. (2000). Ring vaccination. J. Math. Biol., 41, 143\u2013171.","journal-title":"J. Math. Biol."},{"issue":"2","key":"9646_CR24","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1000280","volume":"5","author":"A. Perisic","year":"2009","unstructured":"Perisic, A., & Bauch, C. T. (2009a). Social contact networks and disease eradicability under voluntary vaccination. PLoS Comput. Biol., 5(2), e1000280. doi:10.1371\/journal.pcbi.1000280.","journal-title":"PLoS Comput. Biol."},{"key":"9646_CR25","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1186\/1471-2334-9-77","volume":"9","author":"A. Perisic","year":"2009","unstructured":"Perisic, A., & Bauch, C.T. (2009b). A simulation analysis to characterize the dynamics of vaccinating behaviour on contact networks. BMC Infect. Dis., 9, 77.","journal-title":"BMC Infect. Dis."},{"key":"9646_CR26","doi-asserted-by":"crossref","unstructured":"Rao, N., Mobius, M., & Rosenbalt, T. (2007) Social networks and vaccination decisions. FRB of Boston Working Paper No. 07-12, 1-50.","DOI":"10.2139\/ssrn.1073143"},{"key":"9646_CR27","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.mbs.2006.08.015","volume":"2004","author":"C. T. Reluga","year":"2006","unstructured":"Reluga, C. T., Bauch, C. T., & Galvani, A. P. (2006). Evolving public perceptions and stability in vaccine uptake. Math. Biosci., 2004, 185\u2013198.","journal-title":"Math. Biosci."},{"key":"9646_CR28","first-page":"1505","volume":"2008","author":"M. Salathe","year":"2008","unstructured":"Salathe, M., & Bonhoeffer, S. (2008). The effect of opinion clustering on disease outbreaks. J. R. Soc., 2008, 1505\u20131508.","journal-title":"J. R. Soc."},{"issue":"5","key":"9646_CR29","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.1542\/peds.2006-0923","volume":"118","author":"P. J. Smith","year":"2006","unstructured":"Smith, P. J., Kennedy, A. M., Wooten, K., Gust, D. A., & Pickering, L. K. (2006). Association between health care providers\u2019 influence on parents who have concerns about vaccine safety and vaccination coverage. Pediatrics, 118(5), 1287\u20131292.","journal-title":"Pediatrics"},{"issue":"2","key":"9646_CR30","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0196-6553(82)90003-7","volume":"10","author":"M.\u00a0A. Strassburg","year":"1982","unstructured":"Strassburg, M.\u00a0A. (1982). The global eradication of smallpox. Am. J. Infect. Control, 10(2), 53\u201359.","journal-title":"Am. J. Infect. Control"},{"key":"9646_CR31","doi-asserted-by":"publisher","first-page":"1705","DOI":"10.1016\/S0277-9536(99)00239-7","volume":"49","author":"P. Streefland","year":"1999","unstructured":"Streefland, P., Chowdhury, A. M. R., & Ramos-Jimenez, P. (1999). Patterns of vaccination acceptance. Soc. Sci. Med., 49, 1705\u20131716.","journal-title":"Soc. Sci. Med."},{"issue":"6","key":"9646_CR32","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1097\/00004703-200512000-00009","volume":"26","author":"L. A. Sturm","year":"2005","unstructured":"Sturm, L. A., Mays, R. M., & Zimet, G. D. (2005). Parental beliefs and decision making about child and adolescent immunization: from polio to sexually transmitted infections. J. Dev. Behav. Pediatr., 26(6), 441\u2013452.","journal-title":"J. Dev. Behav. Pediatr."},{"key":"9646_CR33","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/S0147-9571(02)00032-2","volume":"25","author":"B. Toma","year":"2002","unstructured":"Toma, B., Moutou, F., Dufourc, B., & Durand, B. (2002). Ring vaccination against foot-and-mouth disease. Comp. Immunol. Microbiol. Infect. Dis., 25, 365\u2013372.","journal-title":"Comp. Immunol. Microbiol. Infect. Dis."},{"key":"9646_CR34","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s10867-008-9060-9","volume":"34","author":"D. H. Zanette","year":"2008","unstructured":"Zanette, D. H., & Gusman, S. R. (2008). Infection spreading in a population with evolving contacts. J. Biol. Phys., 34, 135\u2013148.","journal-title":"J. Biol. Phys."},{"key":"9646_CR35","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1503\/cmaj.091641","volume":"181","author":"M. Zivkovic Gojovic","year":"2009","unstructured":"Zivkovic Gojovic, M., Sander, B., Fisman, D., Krahn, M., & Bauch, C. T. (2009). Modelling mitigation strategies for pandemic (H1N1) 2009. CMAJ, 181, 673\u2013680.","journal-title":"CMAJ"}],"updated-by":[{"DOI":"10.1007\/s11538-014-0008-x","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2014,10,16]],"date-time":"2014-10-16T00:00:00Z","timestamp":1413417600000}}],"container-title":["Bulletin of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-011-9646-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11538-011-9646-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-011-9646-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-011-9646-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T03:29:12Z","timestamp":1744169352000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11538-011-9646-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,16]]},"references-count":35,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2011,11]]}},"alternative-id":["9646"],"URL":"https:\/\/doi.org\/10.1007\/s11538-011-9646-4","relation":{},"ISSN":["0092-8240","1522-9602"],"issn-type":[{"value":"0092-8240","type":"print"},{"value":"1522-9602","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3,16]]},"assertion":[{"value":"3 September 2010","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 February 2011","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2011","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}