{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T19:54:39Z","timestamp":1778615679159,"version":"3.51.4"},"reference-count":22,"publisher":"Wiley","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301474"],"award-info":[{"award-number":["11301474"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171295"],"award-info":[{"award-number":["11171295"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Yq2013163"],"award-info":[{"award-number":["Yq2013163"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51508319"],"award-info":[{"award-number":["51508319"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61374195"],"award-info":[{"award-number":["61374195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51409157"],"award-info":[{"award-number":["51409157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["07@ZH005"],"award-info":[{"award-number":["07@ZH005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Y201327642"],"award-info":[{"award-number":["Y201327642"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301474"],"award-info":[{"award-number":["11301474"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171295"],"award-info":[{"award-number":["11171295"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Yq2013163"],"award-info":[{"award-number":["Yq2013163"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51508319"],"award-info":[{"award-number":["51508319"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61374195"],"award-info":[{"award-number":["61374195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51409157"],"award-info":[{"award-number":["51409157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["07@ZH005"],"award-info":[{"award-number":["07@ZH005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Y201327642"],"award-info":[{"award-number":["Y201327642"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China","award":["11301474"],"award-info":[{"award-number":["11301474"]}]},{"name":"Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China","award":["11171295"],"award-info":[{"award-number":["11171295"]}]},{"name":"Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China","award":["Yq2013163"],"award-info":[{"award-number":["Yq2013163"]}]},{"name":"Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China","award":["51508319"],"award-info":[{"award-number":["51508319"]}]},{"name":"Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China","award":["61374195"],"award-info":[{"award-number":["61374195"]}]},{"name":"Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China","award":["51409157"],"award-info":[{"award-number":["51409157"]}]},{"name":"Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China","award":["07@ZH005"],"award-info":[{"award-number":["07@ZH005"]}]},{"name":"Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China","award":["Y201327642"],"award-info":[{"award-number":["Y201327642"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301474"],"award-info":[{"award-number":["11301474"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171295"],"award-info":[{"award-number":["11171295"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Yq2013163"],"award-info":[{"award-number":["Yq2013163"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51508319"],"award-info":[{"award-number":["51508319"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61374195"],"award-info":[{"award-number":["61374195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51409157"],"award-info":[{"award-number":["51409157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["07@ZH005"],"award-info":[{"award-number":["07@ZH005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Y201327642"],"award-info":[{"award-number":["Y201327642"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301474"],"award-info":[{"award-number":["11301474"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171295"],"award-info":[{"award-number":["11171295"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Yq2013163"],"award-info":[{"award-number":["Yq2013163"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51508319"],"award-info":[{"award-number":["51508319"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61374195"],"award-info":[{"award-number":["61374195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51409157"],"award-info":[{"award-number":["51409157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["07@ZH005"],"award-info":[{"award-number":["07@ZH005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Y201327642"],"award-info":[{"award-number":["Y201327642"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301474"],"award-info":[{"award-number":["11301474"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171295"],"award-info":[{"award-number":["11171295"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Yq2013163"],"award-info":[{"award-number":["Yq2013163"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51508319"],"award-info":[{"award-number":["51508319"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61374195"],"award-info":[{"award-number":["61374195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51409157"],"award-info":[{"award-number":["51409157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["07@ZH005"],"award-info":[{"award-number":["07@ZH005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Y201327642"],"award-info":[{"award-number":["Y201327642"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Special Authorized Social Science Fund of China","award":["11301474"],"award-info":[{"award-number":["11301474"]}]},{"name":"National Special Authorized Social Science Fund of China","award":["11171295"],"award-info":[{"award-number":["11171295"]}]},{"name":"National Special Authorized Social Science Fund of China","award":["Yq2013163"],"award-info":[{"award-number":["Yq2013163"]}]},{"name":"National Special Authorized Social Science Fund of China","award":["51508319"],"award-info":[{"award-number":["51508319"]}]},{"name":"National Special Authorized Social Science Fund of China","award":["61374195"],"award-info":[{"award-number":["61374195"]}]},{"name":"National Special Authorized Social Science Fund of China","award":["51409157"],"award-info":[{"award-number":["51409157"]}]},{"name":"National Special Authorized Social Science Fund of China","award":["07@ZH005"],"award-info":[{"award-number":["07@ZH005"]}]},{"name":"National Special Authorized Social Science Fund of China","award":["Y201327642"],"award-info":[{"award-number":["Y201327642"]}]},{"name":"Nature and Science Fund from Zhejiang Province Ministry of Education","award":["11301474"],"award-info":[{"award-number":["11301474"]}]},{"name":"Nature and Science Fund from Zhejiang Province Ministry of Education","award":["11171295"],"award-info":[{"award-number":["11171295"]}]},{"name":"Nature and Science Fund from Zhejiang Province Ministry of Education","award":["Yq2013163"],"award-info":[{"award-number":["Yq2013163"]}]},{"name":"Nature and Science Fund from Zhejiang Province Ministry of Education","award":["51508319"],"award-info":[{"award-number":["51508319"]}]},{"name":"Nature and Science Fund from Zhejiang Province Ministry of Education","award":["61374195"],"award-info":[{"award-number":["61374195"]}]},{"name":"Nature and Science Fund from Zhejiang Province Ministry of Education","award":["51409157"],"award-info":[{"award-number":["51409157"]}]},{"name":"Nature and Science Fund from Zhejiang Province Ministry of Education","award":["07@ZH005"],"award-info":[{"award-number":["07@ZH005"]}]},{"name":"Nature and Science Fund from Zhejiang Province Ministry of Education","award":["Y201327642"],"award-info":[{"award-number":["Y201327642"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>A time-delayed mathematical model for tumor growth with the effect of periodic therapy is studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a time delay in cell proliferation process. Sufficient conditions for the global stability of tumor free equilibrium are given. We also prove that if external concentration of nutrients is large the tumor will not disappear and the conditions under which there exist periodic solutions to the model are also determined. Results are illustrated by computer simulations.<\/jats:p>","DOI":"10.1155\/2016\/3643019","type":"journal-article","created":{"date-parts":[[2016,5,5]],"date-time":"2016-05-05T17:01:26Z","timestamp":1462467686000},"page":"1-8","source":"Crossref","is-referenced-by-count":8,"title":["A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy"],"prefix":"10.1155","volume":"2016","author":[{"given":"Shihe","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong 526061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangqing","family":"Wei","sequence":"additional","affiliation":[{"name":"Teaching Research Administration of Guangrao County, Dongying, Shandong 257300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fangwei","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Transport and Communications, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/s0025-5564(97)00023-0"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(94)00117-3"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(96)00023-5"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1972514317"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2007.02.030"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1006\/bulm.1999.0089"},{"key":"22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imammb\/15.1.1","volume":"15","year":"1998","journal-title":"IMA Journal of Mathematics Applied in Medicine and Biology"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/s0025-5564(99)00063-2"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-004-0483-3"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.02.047"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s002850050149"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2005.2.461"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/s0252-9602(06)60104-5"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2004.06.022"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/s0895-7177(03)80019-5"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/s0895-7177(03)00131-6"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2012.02.034"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1515\/apam-2014-0030"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/s0893-9659(00)00061-6"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-00547-7"},{"key":"16","year":"1988"},{"key":"18","year":"1964"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2016\/3643019.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2016\/3643019.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2016\/3643019.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T08:50:31Z","timestamp":1498294231000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/cmmm\/2016\/3643019\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":22,"alternative-id":["3643019","3643019"],"URL":"https:\/\/doi.org\/10.1155\/2016\/3643019","relation":{},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"value":"1748-670X","type":"print"},{"value":"1748-6718","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]}}}