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First, we obtain the existence and uniqueness of the system and the regularity of the solution semiflow based on some assumptions for the parameters. Then, we calculate the basic reproduction number, which is the spectral radius of the next\u2010generation operator. Second, we investigate the existence and local stability of the steady states. Finally, we construct suitable Lyapunov functionals to strictly prove the global stability of the system, which are determined by the basic reproduction number \u211b<jats:sub>0<\/jats:sub> and some assumptions for the incidence rate.<\/jats:p>","DOI":"10.1155\/2018\/9613807","type":"journal-article","created":{"date-parts":[[2018,10,14]],"date-time":"2018-10-14T23:31:57Z","timestamp":1539559917000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age\u2010Dependent Susceptibility"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5825-3364","authenticated-orcid":false,"given":"Junyuan","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6870-6048","authenticated-orcid":false,"given":"Xiaoyan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,10,14]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/hxx020"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2017151"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0092-8240(05)80040-0"},{"key":"e_1_2_10_4_2","first-page":"57","article-title":"Contributions to the mathematical theory of epidemics\u2014II. 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