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Rigorous mathematical results are presented for the proposed models. The local and global dynamics of each model are presented and proven that when [Formula: see text], then the disease-free equilibrium of each model is stable both locally and globally, and when [Formula: see text], then the endemic equilibrium is stable both locally and globally. The numerical results obtained for the proposed model shows that influenza could be eliminated from the community if the threshold is not greater than unity. <\/jats:p>","DOI":"10.1142\/s179396232050035x","type":"journal-article","created":{"date-parts":[[2020,6,9]],"date-time":"2020-06-09T13:41:50Z","timestamp":1591710110000},"page":"2050035","source":"Crossref","is-referenced-by-count":18,"title":["Modeling and scientific computing for the transmission dynamics of Avian influenza with half-saturated incidence"],"prefix":"10.1142","volume":"11","author":[{"given":"Muhammad Altaf","family":"Khan","sequence":"first","affiliation":[{"name":"Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam"},{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saif","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasir","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Farhan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,8,17]]},"reference":[{"key":"S179396232050035XBIB002","doi-asserted-by":"publisher","DOI":"10.1093\/oxfordjournals.bmb.a071538"},{"key":"S179396232050035XBIB003","doi-asserted-by":"publisher","DOI":"10.3201\/eid1201.051254"},{"key":"S179396232050035XBIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s12064-013-0183-6"},{"key":"S179396232050035XBIB008","doi-asserted-by":"publisher","DOI":"10.1137\/030600370"},{"key":"S179396232050035XBIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-007-9257-2"},{"key":"S179396232050035XBIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2005.11.026"},{"key":"S179396232050035XBIB011","doi-asserted-by":"publisher","DOI":"10.1136\/jech.2005.034082"},{"key":"S179396232050035XBIB012","doi-asserted-by":"publisher","DOI":"10.1093\/aje\/kwh092"},{"key":"S179396232050035XBIB013","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2006.0186"},{"key":"S179396232050035XBIB014","doi-asserted-by":"publisher","DOI":"10.1080\/00207160701769625"},{"key":"S179396232050035XBIB015","first-page":"1","volume":"133","author":"Kaddar A.","year":"2009","journal-title":"Electron. 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