Global stability of the endemic equilibrium of a discrete SIR epidemic model

The basic reproductive number [Formula: see text] of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asymptotically stable if [Formula: see text], and the persistence of the model is obtained when...

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Detalles Bibliográficos
Autores principales: Ma, Xia, Zhou, Yicang, Cao, Hui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2013
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100002/
https://www.ncbi.nlm.nih.gov/pubmed/32226446
http://dx.doi.org/10.1186/1687-1847-2013-42
Descripción
Sumario:The basic reproductive number [Formula: see text] of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asymptotically stable if [Formula: see text], and the persistence of the model is obtained when [Formula: see text]. The main attention is paid to the global stability of the endemic equilibrium. Sufficient conditions for the global stability of the endemic equilibrium are established by using the comparison principle. Numerical simulations are done to show our theoretical results and to demonstrate the complicated dynamics of the model. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1687-1847-2013-42) contains supplementary material, which is available to authorized users.

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