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Analysis of a Delayed SIR Model with Nonlinear Incidence Rate
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-01-27
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
An SIR epidemic model with incubation time and saturated incidence rate is formulated, where the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible.
The threshold value ℜ0 determining whether the disease dies out is found.
The results obtained show that the global dynamics are completely determined by the values of the threshold value ℜ0 and time delay (i.e., incubation time length).
If ℜ0 is less than one, the disease-free equilibrium is globally asymptotically stable and the disease always dies out, while if it exceeds one there will be an endemic.
By using the time delay as a bifurcation parameter, the local stability for the endemic equilibrium is investigated, and the conditions with respect to the system to be absolutely stable and conditionally stable are derived.
Numerical results demonstrate that the system with time delay exhibits rich complex dynamics, such as quasiperiodic and chaotic patterns.
American Psychological Association (APA)
2009. Analysis of a Delayed SIR Model with Nonlinear Incidence Rate. Discrete Dynamics in Nature and Society،Vol. 2008, no. 2008, pp.1-16.
https://search.emarefa.net/detail/BIM-487025
Modern Language Association (MLA)
Analysis of a Delayed SIR Model with Nonlinear Incidence Rate. Discrete Dynamics in Nature and Society No. 2008 (2008), pp.1-16.
https://search.emarefa.net/detail/BIM-487025
American Medical Association (AMA)
Analysis of a Delayed SIR Model with Nonlinear Incidence Rate. Discrete Dynamics in Nature and Society. 2009. Vol. 2008, no. 2008, pp.1-16.
https://search.emarefa.net/detail/BIM-487025
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-487025