{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T14:50:09Z","timestamp":1763563809979,"version":"3.41.2"},"reference-count":16,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,7,5]],"date-time":"2012-07-05T00:00:00Z","timestamp":1341446400000},"content-version":"vor","delay-in-days":186,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"name":"South African Herbal Science and Medicines Institute"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We present a model for an SIR epidemic in a population consisting of two components\u2014locals and migrants. We identify three equilibrium points and we analyse the stability of the disease free equilibrium. Then we apply optimal control theory to find an optimal vaccination strategy for this 2\u2010group population in a very simple form. Finally we support our analysis by numerical simulation using the fourth order Runge\u2010Kutta method.<\/jats:p>","DOI":"10.1155\/2012\/275902","type":"journal-article","created":{"date-parts":[[2012,7,5]],"date-time":"2012-07-05T06:16:30Z","timestamp":1341468990000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Modeling the Dynamics of an Epidemic under Vaccination in Two Interacting Populations"],"prefix":"10.1155","volume":"2012","author":[{"given":"Ibrahim H. I.","family":"Ahmed","sequence":"first","affiliation":[]},{"given":"Peter J.","family":"Witbooi","sequence":"additional","affiliation":[]},{"given":"Kailash","family":"Patidar","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,5]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1001776926167"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.09.005"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2008.05.026"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tpb.2007.12.007"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2008.09.013"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.15388\/Informatica.2011.330"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/350892"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.15388\/NA.16.2.14104"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.15388\/NA.16.1.14115"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.biosystems.2008.05.004"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2005.01.030"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.06.050"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.90.24.11698"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.02.041"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10441-010-9095-8"},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011418"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/275902.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/275902.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/275902","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:10:05Z","timestamp":1718089805000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/275902"}},"subtitle":[],"editor":[{"given":"Livija","family":"Cveticanin","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/275902"],"URL":"https:\/\/doi.org\/10.1155\/2012\/275902","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-12-12","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-18","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-07-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"275902"}}