Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate

Y Kyrychko; KB Blyuss

doi:10.1016/j.nonrwa.2004.10.001

Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate

Y Kyrychko
, KB Blyuss

Research output: Contribution to journal › Article (Academic Journal) › peer-review

158 Citations (Scopus)

Abstract

We derive and study a time-delayed SIR model with a general incidence rate. The time delay represents temporary immunity period, i.e. time from recovery to becoming susceptible again. Both trivial and endemic equilibria are found, and their stability is investigated. Using Lyapunov functional approach, the global stability of an endemic equilibrium is shown. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

Translated title of the contribution	Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate
Original language	English
Pages (from-to)	495 - 507
Number of pages	13
Journal	Nonlinear Analysis - Real World Applications
Volume	6 (3)
DOIs	https://doi.org/10.1016/j.nonrwa.2004.10.001
Publication status	Published - Jul 2005

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Publisher: Pergamon-Elsevier Science Ltd

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10.1016/j.nonrwa.2004.10.001

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@article{3456486ef99a4416aac06b7597b831de,

title = "Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate",

abstract = "We derive and study a time-delayed SIR model with a general incidence rate. The time delay represents temporary immunity period, i.e. time from recovery to becoming susceptible again. Both trivial and endemic equilibria are found, and their stability is investigated. Using Lyapunov functional approach, the global stability of an endemic equilibrium is shown. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.",

author = "Y Kyrychko and KB Blyuss",

note = "Publisher: Pergamon-Elsevier Science Ltd",

year = "2005",

month = jul,

doi = "10.1016/j.nonrwa.2004.10.001",

language = "English",

volume = "6 (3)",

pages = "495 -- 507",

journal = "Nonlinear Analysis - Real World Applications",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate

AU - Kyrychko, Y

AU - Blyuss, KB

N1 - Publisher: Pergamon-Elsevier Science Ltd

PY - 2005/7

Y1 - 2005/7

N2 - We derive and study a time-delayed SIR model with a general incidence rate. The time delay represents temporary immunity period, i.e. time from recovery to becoming susceptible again. Both trivial and endemic equilibria are found, and their stability is investigated. Using Lyapunov functional approach, the global stability of an endemic equilibrium is shown. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

AB - We derive and study a time-delayed SIR model with a general incidence rate. The time delay represents temporary immunity period, i.e. time from recovery to becoming susceptible again. Both trivial and endemic equilibria are found, and their stability is investigated. Using Lyapunov functional approach, the global stability of an endemic equilibrium is shown. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

U2 - 10.1016/j.nonrwa.2004.10.001

DO - 10.1016/j.nonrwa.2004.10.001

M3 - Article (Academic Journal)

VL - 6 (3)

SP - 495

EP - 507

JO - Nonlinear Analysis - Real World Applications

JF - Nonlinear Analysis - Real World Applications

ER -

Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate

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