{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:00Z","timestamp":1740134520640,"version":"3.37.3"},"reference-count":20,"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\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["IRT1226","20124410110001"],"award-info":[{"award-number":["IRT1226","20124410110001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program for Changjiang Scholars and Innovative Research Team in University","award":["IRT1226","20124410110001"],"award-info":[{"award-number":["IRT1226","20124410110001"]}]},{"DOI":"10.13039\/501100013286","name":"Research Fund for the Doctoral Program of Higher Education of China","doi-asserted-by":"crossref","award":["IRT1226","20124410110001"],"award-info":[{"award-number":["IRT1226","20124410110001"]}],"id":[{"id":"10.13039\/501100013286","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain time<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03c4<\/mml:mi><\/mml:mrow><\/mml:math>. The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive number<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>\u2264<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>; if<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>&gt;<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>, then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the time<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>\u03c4<\/mml:mi><\/mml:mrow><\/mml:math>is also addressed.<\/jats:p>","DOI":"10.1155\/2014\/854528","type":"journal-article","created":{"date-parts":[[2014,3,2]],"date-time":"2014-03-02T21:01:29Z","timestamp":1393794089000},"page":"1-9","source":"Crossref","is-referenced-by-count":1,"title":["Dynamical Behavior of a New Epidemiological Model"],"prefix":"10.1155","volume":"2014","author":[{"given":"Zizi","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8351-8571","authenticated-orcid":true,"given":"Zhiming","family":"Guo","sequence":"additional","affiliation":[{"name":"Key Laboratory of Mathematics and Interdisciplinary Science of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(78)90006-8"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2006.09.025"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2010.13.195"},{"year":"1991","key":"1"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/0303-2647(91)90043-K"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2006.3.513"},{"issue":"2","key":"8","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/S0025-5564(98)10057-3","volume":"155","year":"1999","journal-title":"Mathematical Biosciences"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139903430185"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(02)00184-0"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(02)00002-2"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2009.03.088"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.07.102"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(02)00108-6"},{"year":"1998","key":"17"},{"year":"1995","key":"15"},{"volume":"101","year":"1992","series-title":"Translations of Mathematical Monographs","key":"20"},{"year":"1996","key":"13"},{"year":"1977","series-title":"Applied Mathematical Sciences","key":"6"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0396(02)00089-X"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00169563"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/854528.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/854528.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/854528.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,11]],"date-time":"2020-05-11T20:30:36Z","timestamp":1589229036000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/854528\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":20,"alternative-id":["854528","854528"],"URL":"https:\/\/doi.org\/10.1155\/2014\/854528","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}