{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:46:56Z","timestamp":1726440416696},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Fr\u00e9chet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system.<\/jats:p>","DOI":"10.1155\/2015\/838312","type":"journal-article","created":{"date-parts":[[2015,2,24]],"date-time":"2015-02-24T21:03:44Z","timestamp":1424811824000},"page":"1-12","source":"Crossref","is-referenced-by-count":3,"title":["Stability Results for an Age-Structured SIS Epidemic Model with Vector Population"],"prefix":"10.1155","volume":"2015","author":[{"given":"He-Long","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Xinyang Normal University, Henan 464000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing-Yuan","family":"Yu","sequence":"additional","affiliation":[{"name":"Beijing Institute of Information and Control, Beijing 100037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guang-Tian","family":"Zhu","sequence":"additional","affiliation":[{"name":"Academy of Mathematics and System Science, C.A.S., Beijing 100080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61317-3_8"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-006-0015-0"},{"issue":"3","key":"3","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1007\/s11538-006-9166-9","volume":"69","year":"2007","journal-title":"Bulletin of Mathematical Biolog"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-008-9111-8"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.08.027"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5554"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2007.07.005"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1137\/0522069"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-75301-5_1"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00178324"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2009.0386"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.10.009"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1137\/0523034"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/s0362-546x(97)00597-x"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2004.01.005"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2004.02.004"},{"key":"17","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.mbs.2013.10.011","volume":"247","year":"2014","journal-title":"Mathematical Biosciences"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2013.01.044"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5561-1"},{"volume":"123","year":"1980","series-title":"Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","key":"20"},{"issue":"1","key":"21","first-page":"199","volume":"23","year":"1948","journal-title":"American Mathematical Society Translation"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/838312.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/838312.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/838312.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,23]],"date-time":"2017-06-23T06:12:19Z","timestamp":1498198339000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/838312\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":21,"alternative-id":["838312","838312"],"URL":"https:\/\/doi.org\/10.1155\/2015\/838312","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2015]]}}}