{"corpus_id":125272636,"paper_sha":"2c7a517a621627af59a795da8dff9c45d1aaf85f","doi":"10.1016/J.PHYSA.2018.03.012","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2793145660,"dblp_id":null,"acl_id":null,"title":"Extinction and periodic solutions for an impulsive SIR model with incidence rate stochastically perturbed","year":2018,"publication_date":"2018-09-01","venue":"Physica A: Statistical Mechanics and its Applications","journal":{"name":"Physica A: Statistical Mechanics and its Applications","pages":null,"volume":null},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":30,"citation_count":14,"influential_citation_count":0,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Abstract In this paper, we consider an impulsive SIR model with incidence rate stochastically perturbed. First, we prove the existence and uniqueness of the global positive solution by constructing the equivalent system without impulse. Second, we obtain a sufficient condition which determines epidemic to extinct. Then we demonstrate the existence and global attraction of the boundary periodic solution under the certain condition. Finally, we present a sufficient condition which allows the existence of a positive periodic solution.","claims":[{"public_id":"cl_65803a68318a314a773f8b086041845f","status":"active","text":"A sufficient condition is derived for epidemic extinction in the impulsive SIR model with stochastically perturbed incidence rate.","confidence":0.97,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_65803a68318a314a773f8b086041845f"},{"public_id":"cl_18792fb06fdfd11116f2c15fa7162d14","status":"active","text":"A sufficient condition is established for the existence of a positive periodic solution.","confidence":0.96,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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