Global stability of multi-group epidemic models with distributed delays

Michael Y. Li; Zhisheng Shuai; Chuncheng Wang

doi:10.1016/j.jmaa.2009.09.017

Global stability of multi-group epidemic models with distributed delays

Michael Y. Li
, Zhisheng Shuai^*
, Chuncheng Wang

^*Corresponding author for this work

School of Mathematics

University of Alberta

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

181 Scopus citations

Abstract

We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number R₀. More specifically, we prove that, if R₀ ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R₀ > 1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals.

Original language	English
Pages (from-to)	38-47
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	361
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2009.09.017
State	Published - 1 Jan 2010

Keywords

Distributed delay
Global stability
Lyapunov functional
Multi-group model

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10.1016/j.jmaa.2009.09.017

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abstract = "We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals.",

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N2 - We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals.

AB - We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals.

KW - Distributed delay

KW - Global stability

KW - Lyapunov functional

KW - Multi-group model

UR - https://www.scopus.com/pages/publications/70349384940

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DO - 10.1016/j.jmaa.2009.09.017

M3 - 文章

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VL - 361

SP - 38

EP - 47

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Global stability of multi-group epidemic models with distributed delays

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Keywords

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