A delayed SIR epidemic model with saturation incidence and a constant infectious period
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In this paper, an SIR epidemic model with saturation incidence and a time delay describing a constant infectious period is investigated. By analyzing the corresponding characteristic equations, the local stability of a diseasefree equilibrium and an endemic equilibrium is established. When the basic reproduction number is greater than unity, it is proved that the disease is uniformly persistent in the population, and explicit formulae are obtained to estimate the eventual lower bound of the fraction of infectious individuals. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the diseasefree equilibrium is globally asymptotically stable. When the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global attractiveness of the endemic equilibrium. Numerical simulations are carried out to illustrate the main results.
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 Title
 A delayed SIR epidemic model with saturation incidence and a constant infectious period
 Journal

Journal of Applied Mathematics and Computing
Volume 35, Issue 12 , pp 229250
 Cover Date
 20110201
 DOI
 10.1007/s1219000903533
 Print ISSN
 15985865
 Online ISSN
 18652085
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 SIR epidemic model
 Saturation incidence
 Infectious period
 Time delay
 Permanence
 Stability
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 34K60
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