Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate

We consider a delayed SIR epidemic model in which the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible. We investigate the qualitative behaviour of the model and find the conditions that guarantee the asymptotic stability of c...

Full description

Saved in:
Bibliographic Details
Published in:International journal of differential equations 2012-01, Vol.2012 (2012), p.1-13
Main Authors: Rihan, Fathalla A., Anwar, M. Naim
Format: Article
Language:English
Subjects:
Asymptotic properties
Behavior
Differential equations
Epidemics
Gain
Incidence
Infections
Mathematical analysis
Mathematical models
Population density
Steady state
Studies
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a delayed SIR epidemic model in which the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible. We investigate the qualitative behaviour of the model and find the conditions that guarantee the asymptotic stability of corresponding steady states. We present the conditions in the time lag τ in which the DDE model is stable. Hopf bifurcation analysis is also addressed. Numerical simulations are provided in order to illustrate the theoretical results and gain further insight into the behaviour of this system.
ISSN:1687-9643
1687-9651
DOI:10.1155/2012/408637