Permanence of an SIR epidemic model with density dependent birth rate and distributed time delay

Chun Hsien Li; Chiung Chiou Tsai; Suh Yuh Yang

doi:10.1016/j.amc.2011.06.047

Permanence of an SIR epidemic model with density dependent birth rate and distributed time delay

Chun Hsien Li, Chiung Chiou Tsai, Suh Yuh Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper, we investigate the permanence of an SIR epidemic model with a density-dependent birth rate and a distributed time delay. We first consider the attractivity of the disease-free equilibrium and then show that for any time delay, the delayed SIR epidemic model is permanent if and only if an endemic equilibrium exists. Numerical examples are given to illustrate the theoretical analysis. The results obtained are also compared with those from the analog system with a discrete time delay.

Original language	English
Pages (from-to)	1682-1693
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	218
Issue number	5
DOIs	https://doi.org/10.1016/j.amc.2011.06.047
State	Published - 1 Nov 2011

Keywords

Asymptotic stability
Permanence
SIR epidemic model
Time delay

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10.1016/j.amc.2011.06.047

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title = "Permanence of an SIR epidemic model with density dependent birth rate and distributed time delay",

abstract = "In this paper, we investigate the permanence of an SIR epidemic model with a density-dependent birth rate and a distributed time delay. We first consider the attractivity of the disease-free equilibrium and then show that for any time delay, the delayed SIR epidemic model is permanent if and only if an endemic equilibrium exists. Numerical examples are given to illustrate the theoretical analysis. The results obtained are also compared with those from the analog system with a discrete time delay.",

keywords = "Asymptotic stability, Permanence, SIR epidemic model, Time delay",

author = "Li, {Chun Hsien} and Tsai, {Chiung Chiou} and Yang, {Suh Yuh}",

note = "Funding Information: The authors would like to thank the Editor-in-Chief Dr. Melvin Scott and an anonymous referee for their valuable comments and suggestions on revising the paper. This work was supported in part by the National Science Council of Taiwan .",

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T1 - Permanence of an SIR epidemic model with density dependent birth rate and distributed time delay

AU - Li, Chun Hsien

AU - Tsai, Chiung Chiou

AU - Yang, Suh Yuh

N1 - Funding Information: The authors would like to thank the Editor-in-Chief Dr. Melvin Scott and an anonymous referee for their valuable comments and suggestions on revising the paper. This work was supported in part by the National Science Council of Taiwan .

PY - 2011/11/1

Y1 - 2011/11/1

N2 - In this paper, we investigate the permanence of an SIR epidemic model with a density-dependent birth rate and a distributed time delay. We first consider the attractivity of the disease-free equilibrium and then show that for any time delay, the delayed SIR epidemic model is permanent if and only if an endemic equilibrium exists. Numerical examples are given to illustrate the theoretical analysis. The results obtained are also compared with those from the analog system with a discrete time delay.

AB - In this paper, we investigate the permanence of an SIR epidemic model with a density-dependent birth rate and a distributed time delay. We first consider the attractivity of the disease-free equilibrium and then show that for any time delay, the delayed SIR epidemic model is permanent if and only if an endemic equilibrium exists. Numerical examples are given to illustrate the theoretical analysis. The results obtained are also compared with those from the analog system with a discrete time delay.

KW - Asymptotic stability

KW - Permanence

KW - SIR epidemic model

KW - Time delay

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SN - 0096-3003

VL - 218

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EP - 1693

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 5

ER -

Permanence of an SIR epidemic model with density dependent birth rate and distributed time delay

Abstract

Keywords

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