{"title":"Dynamics of a Delayed Epidemic Model with Beddington-Deangelis Incidence Rate and a Constant Infectious Period","authors":"Abdelali Raji Allah, H. Alaoui","doi":"10.5890/jand.2020.12.001","DOIUrl":null,"url":null,"abstract":"In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 1, we see that the disease-free equilibrium is unstable and the endemic equilibrium is permanent and locally asymptotically stable and we give sufficient conditions for the global asymptotic stability of the endemic equilibrium.","PeriodicalId":30638,"journal":{"name":"International Journal of Mathematical Modelling Computations","volume":"9 1","pages":"83-100"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematical Modelling Computations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5890/jand.2020.12.001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 1, we see that the disease-free equilibrium is unstable and the endemic equilibrium is permanent and locally asymptotically stable and we give sufficient conditions for the global asymptotic stability of the endemic equilibrium.
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