{"title":"Analysis of a Stochastic SIR Model with Vaccination and Nonlinear Incidence Rate","authors":"A. El koufi, Jihad Adnani, A. Bennar, N. Yousfi","doi":"10.1155/2019/9275051","DOIUrl":null,"url":null,"abstract":"We expand an SIR epidemic model with vertical and nonlinear incidence rates from a deterministic frame to a stochastic one. The existence of a positive global analytical solution of the proposed stochastic model is shown, and conditions for the extinction and persistence of the disease are established. The presented results are demonstrated by numerical simulations.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2019-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2019/9275051","citationCount":"31","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2019/9275051","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 31
Abstract
We expand an SIR epidemic model with vertical and nonlinear incidence rates from a deterministic frame to a stochastic one. The existence of a positive global analytical solution of the proposed stochastic model is shown, and conditions for the extinction and persistence of the disease are established. The presented results are demonstrated by numerical simulations.
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