Local stability of an SIR epidemic model and effect of time delay

We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria—a necessary condition for local asymptotic stability is give...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2009-11, Vol.32 (16), p.2160-2175
Main Authors: Tchuenche, Jean M., Nwagwo, Alexander
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
local stability
Lyapunov function
Mathematical analysis
Mathematics
Sciences and techniques of general use
SIR model
time delay
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria—a necessary condition for local asymptotic stability is given. The proofs are based on linearization and the application of Lyapunov functional approach. An upper bound of the critical time delay for which the model remains valid is derived. Numerical simulations are carried out to illustrate the effect of time delay which tends to reduce the epidemic threshold. Copyright © 2009 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.1136