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The well-posedness and the basic reproduction number [Formula: see text] of our model are first presented. If [Formula: see text], the drug-free steady state [Formula: see text] is locally stable and there will be multiple positive steady states due to the imperfect vaccine. If [Formula: see text], there is a unique drug spread steady state, and our model is uniformly persistent. To reveal the dynamics of our model in detail, we carry out a further analysis in some special cases, including the backward and forward bifurcation results of our model when [Formula: see text] and [Formula: see text], and the unique drug-spread steady state\u2019s stability when [Formula: see text]. Finally, a brief conclusion and discussion are presented.<\/jats:p>","DOI":"10.1142\/s0218127421501571","type":"journal-article","created":{"date-parts":[[2021,8,13]],"date-time":"2021-08-13T13:11:45Z","timestamp":1628860305000},"page":"2150157","source":"Crossref","is-referenced-by-count":10,"title":["Dynamics of an Age Structured Heroin Transmission Model with Imperfect Vaccination"],"prefix":"10.1142","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2472-8704","authenticated-orcid":false,"given":"Xi-Chao","family":"Duan","sequence":"first","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology, 516 Jun Gong Road, Shanghai 200093, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huanhuan","family":"Cheng","sequence":"additional","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology, 516 Jun Gong Road, Shanghai 200093, P. R. 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