Global stability of multi-group vaccination epidemic models with delays

Deqiong Ding; Xiaohua Ding

doi:10.1016/j.nonrwa.2010.12.015

Global stability of multi-group vaccination epidemic models with delays

Deqiong Ding
, Xiaohua Ding^*

^*Corresponding author for this work

Harbin Institute of Technology Weihai

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

32 Scopus citations

Abstract

In this paper, we investigate a class of multi-group vaccination epidemic models with delays. We show that the global dynamics are determined by the threshold criterion σ(A). We present that when σ(A)<0, there is a unique disease-free equilibrium which is globally asymptotically stable; when σ(A)>0, there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the method of global Lyapunov functionals.

Original language	English
Pages (from-to)	1991-1997
Number of pages	7
Journal	Nonlinear Analysis: Real World Applications
Volume	12
Issue number	4
DOIs	https://doi.org/10.1016/j.nonrwa.2010.12.015
State	Published - Aug 2011
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Graph-theoretic approach
Lyapunov functional
Multi-group epidemic model
Stability

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10.1016/j.nonrwa.2010.12.015

Cite this

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abstract = "In this paper, we investigate a class of multi-group vaccination epidemic models with delays. We show that the global dynamics are determined by the threshold criterion σ(A). We present that when σ(A)<0, there is a unique disease-free equilibrium which is globally asymptotically stable; when σ(A)>0, there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the method of global Lyapunov functionals.",

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AB - In this paper, we investigate a class of multi-group vaccination epidemic models with delays. We show that the global dynamics are determined by the threshold criterion σ(A). We present that when σ(A)<0, there is a unique disease-free equilibrium which is globally asymptotically stable; when σ(A)>0, there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the method of global Lyapunov functionals.

KW - Graph-theoretic approach

KW - Lyapunov functional

KW - Multi-group epidemic model

KW - Stability

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Global stability of multi-group vaccination epidemic models with delays

Abstract

UN SDGs

Keywords

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