{"title":"具有Beddington Deangelis发病率和恒定传染期的延迟流行病模型的动力学","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":"{\"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}","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}
Dynamics of a Delayed Epidemic Model with Beddington-Deangelis Incidence Rate and a Constant Infectious Period
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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