{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T16:56:30Z","timestamp":1777222590977,"version":"3.51.4"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2015,10]]},"abstract":"<jats:p> In this paper, we have formulated a simple SIS type epidemic model in the presence of treatment control, and we have discussed the dynamical behavior of the system. The system is modified by considering both the disease transmission rate and the treatment function as fuzzy numbers, and also the fuzzy expected value of the infected individuals is calculated. Furthermore, the fuzzy basic reproduction number is investigated and a threshold condition of pathogen is obtained at which the system undergoes a transcritical bifurcation. <\/jats:p>","DOI":"10.1142\/s0218488515500282","type":"journal-article","created":{"date-parts":[[2015,10,15]],"date-time":"2015-10-15T06:59:08Z","timestamp":1444892348000},"page":"651-665","source":"Crossref","is-referenced-by-count":44,"title":["Dynamical Behavior of an Epidemic Model in a Fuzzy Transmission"],"prefix":"10.1142","volume":"23","author":[{"given":"Prasanta Kumar","family":"Mondal","sequence":"first","affiliation":[{"name":"Shibpur Sri Ramkrishna Vidyalaya, 92, Kshetra Banerjee Lane, Shibpur, Howrah 711102, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Soovoojeet","family":"Jana","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abhedananda Mahavidyalaya, Sainthia-731234, Birbhum, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Palash","family":"Haldar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sundarban Hazi Desarat College, Dist-24 PGS (S), Pin-743611, Pathankhali, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. K.","family":"Kar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,10,15]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.biosystems.2012.10.003"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218339008002484"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2005.12.022"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2008.10.067"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2007.10.011"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.06.018"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(02)00372-7"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-009-9435-5"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2012.03.010"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1080\/17513758.2010.510584"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1007\/s10441-010-9095-8"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.12.021"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2013.01.022"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1927.0118"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.06.074"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2003.11.043"},{"issue":"2","key":"p_21","first-page":"87","volume":"29","author":"Kar T. K.","year":"2013","journal-title":"Int. J. Ecol. Econ. Statist."},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1007\/s10852-012-9210-8"},{"key":"p_23","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90029-5"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.05.018"},{"key":"p_26","doi-asserted-by":"publisher","DOI":"10.1016\/j.bulm.2004.03.002"},{"key":"p_27","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2012.11.007"},{"key":"p_28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jksus.2012.01.003"},{"key":"p_29","doi-asserted-by":"publisher","DOI":"10.12785\/amis\/070528"},{"key":"p_30","doi-asserted-by":"publisher","DOI":"10.5373\/jaram.1447.051912"}],"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218488515500282","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:04:05Z","timestamp":1565183045000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488515500282"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10]]},"references-count":25,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2015,10,15]]},"published-print":{"date-parts":[[2015,10]]}},"alternative-id":["10.1142\/S0218488515500282"],"URL":"https:\/\/doi.org\/10.1142\/s0218488515500282","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10]]}}}