{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T07:49:19Z","timestamp":1774511359305,"version":"3.50.1"},"reference-count":33,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"5\/6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MBE"],"published-print":{"date-parts":[[2017,5]]},"DOI":"10.3934\/mbe.2017069","type":"journal-article","created":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T13:58:49Z","timestamp":1495807129000},"page":"1337-1360","source":"Crossref","is-referenced-by-count":22,"title":["Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse"],"prefix":"10.3934","volume":"14","author":[{"given":"Shanjing","family":"Ren","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"1","article-title":"<em>Sobolev Spaces<\/em>,","author":"R. A. Adams","year":"2003","journal-title":"Academic Press"},{"key":"2","doi-asserted-by":"publisher","first-page":"1335","DOI":"10.3934\/mbe.2013.10.1335","article-title":"Dynamics of an age-of-infection cholera model,","volume":"10","author":"F. Brauer","year":"2013","journal-title":"<em>Mathematical Biosciences and Engineering<\/em>"},{"key":"3","doi-asserted-by":"publisher","first-page":"449","DOI":"10.3934\/mbe.2014.11.449","article-title":"The global stability of an SIRS model with infection age,","volume":"11","author":"Y. Chen","year":"2014","journal-title":"<em>Mathematical Biosciences and Engineering<\/em>"},{"key":"4","doi-asserted-by":"publisher","first-page":"205","DOI":"10.3934\/mbe.2007.4.205","article-title":"Modeling diseases with latency and relapse,","volume":"4","author":"P. van den Driessche","year":"2007","journal-title":"<em>Mathematical Biosciences and Engineering<\/em>"},{"key":"5","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.mbs.2006.09.017","article-title":"Modeling relapse in infectious diseases,","volume":"207","author":"P. van den Driessche","year":"2007","journal-title":"<em>Mathematical Biosciences<\/em>"},{"key":"6","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1137\/120890351","article-title":"An age-structured within-host model for multistrain malaria infections,","volume":"73","author":"R. D. Demasse","year":"2013","journal-title":"<em>Siam Journal on Applied Mathematics<\/em>"},{"key":"7","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/BF00178324","article-title":"On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations,","volume":"28","author":"O. Diekmann","year":"1990","journal-title":"<em>Mathematical Biology<\/em>"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/025","article-title":"<em>Asymptotic Behavior of Dissipative Systems<\/em>,","author":"J. K. Hale","year":"1988","journal-title":"American Mathematical Society"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0060406","article-title":"<em>Functional Differential Equations<\/em>,","author":"J. K. Hale","year":"1971","journal-title":"Springer"},{"key":"10","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1137\/0520025","article-title":"Persistence in infinite dimensional systems,","volume":"20","author":"J. K. Hale","year":"1989","journal-title":"<em>Siam Journal on Mathematical Analysis<\/em>"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970487","article-title":"<em>Mathematical Theories of Populations: Deomgraphics, Genetics, and Epidemics<\/em>,","author":"F. Hoppensteadt","year":"1975","journal-title":"SIAM"},{"key":"12","article-title":"Mathematical theory of age-structured population dynamics,","volume":"7","author":"M. Iannelli","year":"1994","journal-title":"<em>Applied Mathematics Monagraphs CNR<\/em>"},{"key":"13","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1098\/rspa.1927.0118","article-title":"A contribution to the mathematical theory of epidemics,","volume":"115","author":"W. O. Kermack","year":"1927","journal-title":"<em>Proc. R. Soc. London Ser. A<\/em>"},{"key":"14","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1098\/rspa.1932.0171","article-title":"Contributions to the mathematical theory of epidemics II. The problem of endemicity,","volume":"138","author":"W. O. Kermack","year":"1932","journal-title":"<em>Proc.R. Soc.London Ser. A<\/em>"},{"key":"15","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1098\/rspa.1933.0106","article-title":"Contributions to the mathematical theory of epidemics III. Further studies of the problem of endemicity,","volume":"141","author":"W. O. Kermack","year":"1933","journal-title":"<em>Proc.R. Soc.London Ser. A<\/em>"},{"key":"16","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/0025-5564(95)92756-5","article-title":"Global stability for the SEIR model in epidemilogy,","volume":"125","author":"M. Y. Li","year":"1995","journal-title":"<em>Mathematical Biosciences<\/em>"},{"key":"17","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.nonrwa.2015.01.001","article-title":"Global stability of an SEIR epidemic model with age-dependent latency and relapse,","volume":"24","author":"L. Liu","year":"2015","journal-title":"<em>Nonlinear Analysis<\/em>"},{"key":"18","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1080\/00036810903208122","article-title":"Lyapunov functional and global asymptotic stability for an infection-age model,","volume":"89","author":"P. Magal","year":"2010","journal-title":"<em>Applicable Analysis<\/em>"},{"key":"19","first-page":"229","article-title":"Compact attractors for time-periodic age-structured population models,","volume":"65","author":"P. Magal","year":"2001","journal-title":"<em>Electronic Journal of Differential Equations"},{"key":"20","doi-asserted-by":"publisher","first-page":"819","DOI":"10.3934\/mbe.2012.9.819","article-title":"Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes,","volume":"9","author":"C. C. McCluskey","year":"2012","journal-title":"<em>Mathematical Biosciences and Engineering<\/em>"},{"key":"21","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1017\/S0013091500034428","article-title":"Application of mathematics to medical problems,","volume":"44","author":"A. G. McKendrick","year":"1925","journal-title":"<em>Proceedings of the Edinburgh Mathematical Society<\/em>"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/118","article-title":"<em>Dynamical Systems and Population Persistence,<\/em>","author":"H. L. Smith","year":"2011","journal-title":"American Mathematical Society"},{"key":"23","first-page":"50","article-title":"<em>On the Global Stability of Infectious Diseases Models with Relapse<\/em>,","volume":"9","author":"C. Vargas-De-Le\u00f3n","year":"2013","journal-title":"Abstr. Appl"},{"key":"24","doi-asserted-by":"publisher","first-page":"227","DOI":"10.3934\/mbe.2016.13.227","article-title":"A note on dynamics of an age-of-infection cholera model,","volume":"13","author":"J. Wang","year":"2016","journal-title":"<em>Mathematical Biosciences and Engineering<\/em>"},{"key":"25","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/j.jmaa.2015.06.040","article-title":"Global dynamics for a class of age-infection HIV models with nonlinear infection rate,","volume":"432","author":"J. Wang","year":"2015","journal-title":"<em>Mathematical Analysis and Applications<\/em>"},{"key":"26","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1093\/imamat\/hxv039","article-title":"The dynamics of an SVIR epidemiological model with infection age,","volume":"81","author":"J. Wang","year":"2016","journal-title":"<em>Applied Mathematics<\/em>"},{"key":"27","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1080\/17513758.2015.1006696","article-title":"The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes,","volume":"9","author":"J. Wang*","year":"2015","journal-title":"<em>Biological Dynamics<\/em>"},{"key":"28","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1016\/j.nonrwa.2016.04.009","article-title":"Global dynamics for an age-structured epidemic model with media impact and incomplete vaccination,","volume":"32","author":"L. Wang","year":"2016","journal-title":"<em>Nonlinear Analysis: Real World Applications<\/em>"},{"key":"29","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1155\/2012\/184918","article-title":"A TB model with infectivity in latent period and imperfect treatment,","volume":"2012","author":"J. Wang","year":"2012","journal-title":"<em>Discrete Dynamics in Nature and Society<\/em>"},{"key":"30","article-title":"<em>Theory of Nonlinear Age-Dependent Population Dynamics<\/em>,","author":"G. F. Webb","year":"1985","journal-title":"Marcel Dekker"},{"key":"31","doi-asserted-by":"publisher","first-page":"859","DOI":"10.3934\/mbe.2015.12.859","article-title":"Global stability of age-structured virus dynamics model with Beddinaton-Deangelis infection function,","volume":"12","author":"Y. Yang","year":"2015","journal-title":"<em>Mathematical Biosciences and Engineering<\/em>"},{"key":"32","article-title":"<em>Qualitative Analysis and Data Simulation of Tuberculosis Transmission Models<\/em>,","author":"J. H. Zhang","year":"2014","journal-title":"Ph.D thesis"},{"key":"33","article-title":"<em>Centers for Disease Control and Prevention, Vaccines and Immunizations-Measles Epidemiology and Prevention of Vaccine-Preventable Diseases<\/em>,","journal-title":"Available from: <a href="}],"container-title":["Mathematical Biosciences and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.aimspress.com\/article\/10.3934\/mbe.2017069\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T08:03:46Z","timestamp":1563955426000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimsciences.org\/journals\/displayArticlesnew.jsp?paperID=14164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5]]},"references-count":33,"journal-issue":{"issue":"5\/6","published-print":{"date-parts":[[2017,10]]}},"URL":"https:\/\/doi.org\/10.3934\/mbe.2017069","relation":{},"ISSN":["1551-0018"],"issn-type":[{"value":"1551-0018","type":"print"}],"subject":[],"published":{"date-parts":[[2017,5]]}}}