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A pulse system is built to model this process based on an SI ordinary differential equation model. At first, for the system neglecting the impulse effect, we give the classification of singular points. Then for the pulse system, by using the theory of the semicontinuous dynamic system, the dynamics is analyzed. Our analysis shows that the pulse system exhibits rich dynamics and the system has a unique order-1 homoclinic cycle, and by choosing<jats:italic>p<\/jats:italic>as the control parameter, the order-1 homoclinic cycle disappears and bifurcates an orbitally asymptotical stable order-1 periodic solution when<jats:italic>p<\/jats:italic>changes. Numerical simulations by maple 18 are carried out to illustrate the theoretical results.<\/jats:p>","DOI":"10.1155\/2019\/3859815","type":"journal-article","created":{"date-parts":[[2019,2,6]],"date-time":"2019-02-06T23:30:54Z","timestamp":1549495854000},"page":"1-10","source":"Crossref","is-referenced-by-count":11,"title":["State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2127-0267","authenticated-orcid":true,"given":"Kaiyuan","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Anshan Normal University, Anshan 114016, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9603-3867","authenticated-orcid":true,"given":"Tongqian","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, 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