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The influence of treatment period for a drug consumer before quitting treatment is investigated, where it is obtained that the considered model can undergo backward bifurcation, which shows the possibility of having two endemic equilibriums, this type of bifurcation is discussed in terms of the basic reproduction number [Formula: see text]. The bifurcation diagram is drown in the case of an age structured model. Also, we show the existence of Hopf bifurcation is shown under suitable conditions on the model parameters. The obtained mathematical results are confirmed numerically.<\/jats:p>","DOI":"10.1142\/s1793962321500185","type":"journal-article","created":{"date-parts":[[2020,11,30]],"date-time":"2020-11-30T08:50:15Z","timestamp":1606726215000},"page":"2150018","source":"Crossref","is-referenced-by-count":30,"title":["Backward, Hopf bifurcation in a heroin epidemic model with treat age\u22c6"],"prefix":"10.1142","volume":"12","author":[{"given":"Soufiane","family":"Bentout","sequence":"first","affiliation":[{"name":"Laboratoire d\u2019Analyse Non Lin\u00e9aire et Math\u00e9matiques Appliqu\u00e9es, Universit\u00e9 de Tlemcen, Tlemcen, Algeria"},{"name":"Department of Mathematics and Informatics, Belhadj Bouchaib University Center of Ain, Temouchent, BP 284 RP 46000, Algeria"}]},{"given":"Salih","family":"Djilali","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Analyse Non Lin\u00e9aire et Math\u00e9matiques Appliqu\u00e9es, Universit\u00e9 de Tlemcen, Tlemcen, Algeria"},{"name":"Faculty of Exact and Computer Sciences, Mathematic Department, Hassiba, Benbouali University, Chlef, Algeria"}]},{"given":"Behzad","family":"Ghanbari","sequence":"additional","affiliation":[{"name":"Department of Basic Science, Kermanshah University of Technology, Kermanshah, Iran"}]}],"member":"219","published-online":{"date-parts":[[2021,1,12]]},"reference":[{"key":"S1793962321500185BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2006.10.008"},{"key":"S1793962321500185BIB002","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.amc.2015.04.055","volume":"263","author":"Fang B.","year":"2015","journal-title":"Appl. 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