{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T12:37:37Z","timestamp":1771677457089,"version":"3.50.1"},"reference-count":20,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T00:00:00Z","timestamp":1577059200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2019,12,23]]},"abstract":"<jats:p>In this study, we develop and analyze a deterministic mathematical model for tuberculosis (TB) transmission dynamics. The model includes vaccination for newborns and treatment for both high-risk latent and active TB patients. The stability of disease-free equilibrium point is discussed in detail. In the numerical simulation, the model parameters are estimated using reported TB incidence data in Ethiopia from the years 2003 to 2017, and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math> is calculated as <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>\u2248<\/mml:mo><mml:mn>2.13<\/mml:mn><\/mml:mrow><\/mml:math>. Finally, the sensitivity indices of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math> with respect to the model parameters are performed, and their corresponding graphical results are presented. Our results quantify the positive influence of vaccination and the treatment for high-risk latent and active TB patients on the control of tuberculosis.<\/jats:p>","DOI":"10.1155\/2019\/7463167","type":"journal-article","created":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T18:31:12Z","timestamp":1577125872000},"page":"1-9","source":"Crossref","is-referenced-by-count":12,"title":["Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics"],"prefix":"10.1155","volume":"2019","author":[{"given":"Ashenafi","family":"Kelemu Mengistu","sequence":"first","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1304-0282","authenticated-orcid":true,"given":"Peter J.","family":"Witbooi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa"}]}],"member":"311","reference":[{"key":"2","year":"2008"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.g4643"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.2105\/ajph.52.6.1002"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1186\/s13104-017-2968-z"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.3844\/jmssp.2005.217.224"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.tpb.2007.12.007"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s40435-013-0020-2"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0206603"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.3390\/ijerph14101192"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-014-9962-6"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2014.06.037"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2018.01.026"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.biosystems.2014.10.002"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s10441-017-9308-5"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-017-1166-6"},{"key":"20","year":"2002"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2019.03.012"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1001\/jama.1994.03510330076038"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-008-9299-0"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/j.idm.2017.06.002"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2019\/7463167.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2019\/7463167.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2019\/7463167.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T18:31:13Z","timestamp":1577125873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jam\/2019\/7463167\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,23]]},"references-count":20,"alternative-id":["7463167","7463167"],"URL":"https:\/\/doi.org\/10.1155\/2019\/7463167","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,23]]}}}