Dynamic behaviors of a delayed HIV model with stage-structure

Pengmiao Hao; Dejun Fan; Junjie Wei; Qinghe Liu

doi:10.1016/j.cnsns.2012.04.004

Dynamic behaviors of a delayed HIV model with stage-structure

Pengmiao Hao
, Dejun Fan^*
, Junjie Wei
, Qinghe Liu

^*Corresponding author for this work

Harbin Institute of Technology Weihai
Automotive Engineering College

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

8 Scopus citations

Abstract

Inspired by a simulation specific to a delayed HIV model with stage-structure, some dynamic behaviors are studied in this paper, including global stability of disease-free equilibrium and local Hopf bifurcation when taking the delay as a parameter. The corresponding characteristic equation is a transcendental equation, with the parameters delay-dependent, thus we use the conventional analysis introduced by Beretta and Kuang to obtain sufficient conditions to the existence of Hopf bifurcation. Then some properties of Hopf bifurcation such as direction, stability and period are determined, and several examples illustrate our results.

Original language	English
Pages (from-to)	4753-4766
Number of pages	14
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	17
Issue number	12
DOIs	https://doi.org/10.1016/j.cnsns.2012.04.004
State	Published - Dec 2012
Externally published	Yes

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

HIV model
Hopf bifurcation
Stage-structure
Time delay

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10.1016/j.cnsns.2012.04.004

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title = "Dynamic behaviors of a delayed HIV model with stage-structure",

abstract = "Inspired by a simulation specific to a delayed HIV model with stage-structure, some dynamic behaviors are studied in this paper, including global stability of disease-free equilibrium and local Hopf bifurcation when taking the delay as a parameter. The corresponding characteristic equation is a transcendental equation, with the parameters delay-dependent, thus we use the conventional analysis introduced by Beretta and Kuang to obtain sufficient conditions to the existence of Hopf bifurcation. Then some properties of Hopf bifurcation such as direction, stability and period are determined, and several examples illustrate our results.",

keywords = "HIV model, Hopf bifurcation, Stage-structure, Time delay",

author = "Pengmiao Hao and Dejun Fan and Junjie Wei and Qinghe Liu",

year = "2012",

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TY - JOUR

T1 - Dynamic behaviors of a delayed HIV model with stage-structure

AU - Hao, Pengmiao

AU - Fan, Dejun

AU - Wei, Junjie

AU - Liu, Qinghe

PY - 2012/12

Y1 - 2012/12

N2 - Inspired by a simulation specific to a delayed HIV model with stage-structure, some dynamic behaviors are studied in this paper, including global stability of disease-free equilibrium and local Hopf bifurcation when taking the delay as a parameter. The corresponding characteristic equation is a transcendental equation, with the parameters delay-dependent, thus we use the conventional analysis introduced by Beretta and Kuang to obtain sufficient conditions to the existence of Hopf bifurcation. Then some properties of Hopf bifurcation such as direction, stability and period are determined, and several examples illustrate our results.

AB - Inspired by a simulation specific to a delayed HIV model with stage-structure, some dynamic behaviors are studied in this paper, including global stability of disease-free equilibrium and local Hopf bifurcation when taking the delay as a parameter. The corresponding characteristic equation is a transcendental equation, with the parameters delay-dependent, thus we use the conventional analysis introduced by Beretta and Kuang to obtain sufficient conditions to the existence of Hopf bifurcation. Then some properties of Hopf bifurcation such as direction, stability and period are determined, and several examples illustrate our results.

KW - HIV model

KW - Hopf bifurcation

KW - Stage-structure

KW - Time delay

UR - https://www.scopus.com/pages/publications/84864414005

U2 - 10.1016/j.cnsns.2012.04.004

DO - 10.1016/j.cnsns.2012.04.004

M3 - 文章

AN - SCOPUS:84864414005

SN - 1007-5704

VL - 17

SP - 4753

EP - 4766

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 12

ER -

Dynamic behaviors of a delayed HIV model with stage-structure

Abstract

UN SDGs

Keywords

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