{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:32:26Z","timestamp":1767339146585,"version":"3.37.3"},"reference-count":19,"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":[{"name":"Doctorial Subjects Foundation of The Ministry of Education of China","award":["2013651110001","11271312","11401512","11261056"],"award-info":[{"award-number":["2013651110001","11271312","11401512","11261056"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2013651110001","11271312","11401512","11261056"],"award-info":[{"award-number":["2013651110001","11271312","11401512","11261056"]}],"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":["2013651110001","11271312","11401512","11261056"],"award-info":[{"award-number":["2013651110001","11271312","11401512","11261056"]}],"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":["2013651110001","11271312","11401512","11261056"],"award-info":[{"award-number":["2013651110001","11271312","11401512","11261056"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold value<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>. That is, when<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:msub><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>&lt;<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:math>and together with an additional condition, the disease is extinct with probability one, and when<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>&gt;<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:math>, the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, when<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:msub><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>&gt;<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:math>, the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems.<\/jats:p>","DOI":"10.1155\/2016\/5218163","type":"journal-article","created":{"date-parts":[[2016,6,23]],"date-time":"2016-06-23T19:27:37Z","timestamp":1466710057000},"page":"1-14","source":"Crossref","is-referenced-by-count":9,"title":["The Dynamical Behaviors in a Stochastic SIS Epidemic Model with Nonlinear Incidence"],"prefix":"10.1155","volume":"2016","author":[{"given":"Ramziya","family":"Rifhat","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qing","family":"Ge","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhidong","family":"Teng","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(97)00106-7"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(01)00089-X"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.02.057"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.11.005"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.01.055"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1137\/10081856x"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.11.072"},{"issue":"1","key":"9","doi-asserted-by":"crossref","first-page":"59","DOI":"10.15388\/NA.16.1.14115","volume":"16","year":"2011","journal-title":"Nonlinear Analysis: Modelling and Control"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2013.06.009"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2014.01.158"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2012.12.021"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2015.08.024"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2014.11.1003"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1080\/07362994.2014.961088"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2014.06.003"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2014.03.037"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1533\/9780857099402"},{"year":"1980","key":"10"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1137\/s0036144500378302"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2016\/5218163.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2016\/5218163.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2016\/5218163.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T23:57:41Z","timestamp":1568073461000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/cmmm\/2016\/5218163\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":19,"alternative-id":["5218163","5218163"],"URL":"https:\/\/doi.org\/10.1155\/2016\/5218163","relation":{},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"type":"print","value":"1748-670X"},{"type":"electronic","value":"1748-6718"}],"subject":[],"published":{"date-parts":[[2016]]}}}