{"title":"具有治疗的离散SEIR流行病模型的全局动力学","authors":"M. DarAssi, Mohammad-Ayman A. Safi","doi":"10.5269/bspm.62203","DOIUrl":null,"url":null,"abstract":"The global dynamics of a discrete SEIR epidemic model with treatment has been considered. A unique positive solution for the proposed model with the positive initial conditions is obtained. The stability analysis of the disease-free equilibrium and endemic equilibrium have been investigated. It has been proved that the DFE is globally asymptotically stable when the basic reproduction number $\\mathcal{R}_0\\leq1$. The proposed model has a unique endemic equilibrium that is globally asymptotically stable whenever $\\tilde{\\mathcal{R}}_0>1$. The theoretical results are illustrated by a numerical simulation.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global dynamics of a discrete SEIR epidemic model with treatment\",\"authors\":\"M. DarAssi, Mohammad-Ayman A. Safi\",\"doi\":\"10.5269/bspm.62203\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The global dynamics of a discrete SEIR epidemic model with treatment has been considered. A unique positive solution for the proposed model with the positive initial conditions is obtained. The stability analysis of the disease-free equilibrium and endemic equilibrium have been investigated. It has been proved that the DFE is globally asymptotically stable when the basic reproduction number $\\\\mathcal{R}_0\\\\leq1$. The proposed model has a unique endemic equilibrium that is globally asymptotically stable whenever $\\\\tilde{\\\\mathcal{R}}_0>1$. The theoretical results are illustrated by a numerical simulation.\",\"PeriodicalId\":44941,\"journal\":{\"name\":\"Boletim Sociedade Paranaense de Matematica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Boletim Sociedade Paranaense de Matematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5269/bspm.62203\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boletim Sociedade Paranaense de Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5269/bspm.62203","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Global dynamics of a discrete SEIR epidemic model with treatment
The global dynamics of a discrete SEIR epidemic model with treatment has been considered. A unique positive solution for the proposed model with the positive initial conditions is obtained. The stability analysis of the disease-free equilibrium and endemic equilibrium have been investigated. It has been proved that the DFE is globally asymptotically stable when the basic reproduction number $\mathcal{R}_0\leq1$. The proposed model has a unique endemic equilibrium that is globally asymptotically stable whenever $\tilde{\mathcal{R}}_0>1$. The theoretical results are illustrated by a numerical simulation.