Asymptotic dynamics for an age-structured HIV model with two delays

Yuan Yuan; Jialiang Huang; Dongxue Yan; Xianlong Fu

doi:10.1093/imamat/hxag008

Asymptotic dynamics for an age-structured HIV model with two delays

Yuan Yuan
, Jialiang Huang
, Dongxue Yan
, Xianlong Fu^*

^*Corresponding author for this work

School of Mathematical Sciences

Nanjing University of Finance & Economics
Zhejiang Normal University
Nanjing University of Posts and Telecommunications

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

Abstract

This paper deals with an age-structured HIV model with antiretrowviral therapy and two infection routes (virus-to-cell and cell-to-cell). The model is first formulated as an abstract non-densely defined Cauchy problem and the existence of the equilibria is obtained under some conditions. Based on the existence of equilibria, the global asymptotical stability of the disease-free equilibrium is studied by applying theory of operator semigroups and spectral analysis. The stability and Hopf bifurcation results with two delays around the endemic equilibrium are also well described under some conditions by the geometric stability switch criteria. Finally some numerical examples are presented to illustrate the obtained results.

Original language	English
Pages (from-to)	86-117
Number of pages	32
Journal	IMA Journal of Applied Mathematics
Volume	91
Issue number	1
DOIs	https://doi.org/10.1093/imamat/hxag008
State	Published - Jan 2026

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

C-semigroup
Hopf bifurcation
age-structured HIV model
asymptotical stability
time delays

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10.1093/imamat/hxag008

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title = "Asymptotic dynamics for an age-structured HIV model with two delays",

abstract = "This paper deals with an age-structured HIV model with antiretrowviral therapy and two infection routes (virus-to-cell and cell-to-cell). The model is first formulated as an abstract non-densely defined Cauchy problem and the existence of the equilibria is obtained under some conditions. Based on the existence of equilibria, the global asymptotical stability of the disease-free equilibrium is studied by applying theory of operator semigroups and spectral analysis. The stability and Hopf bifurcation results with two delays around the endemic equilibrium are also well described under some conditions by the geometric stability switch criteria. Finally some numerical examples are presented to illustrate the obtained results.",

keywords = "C-semigroup, Hopf bifurcation, age-structured HIV model, asymptotical stability, time delays",

author = "Yuan Yuan and Jialiang Huang and Dongxue Yan and Xianlong Fu",

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year = "2026",

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doi = "10.1093/imamat/hxag008",

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AU - Yuan, Yuan

AU - Huang, Jialiang

AU - Yan, Dongxue

AU - Fu, Xianlong

N1 - Publisher Copyright: © The Author(s) 2026. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/pages/standard-publication-reuse-rights)

PY - 2026/1

Y1 - 2026/1

N2 - This paper deals with an age-structured HIV model with antiretrowviral therapy and two infection routes (virus-to-cell and cell-to-cell). The model is first formulated as an abstract non-densely defined Cauchy problem and the existence of the equilibria is obtained under some conditions. Based on the existence of equilibria, the global asymptotical stability of the disease-free equilibrium is studied by applying theory of operator semigroups and spectral analysis. The stability and Hopf bifurcation results with two delays around the endemic equilibrium are also well described under some conditions by the geometric stability switch criteria. Finally some numerical examples are presented to illustrate the obtained results.

AB - This paper deals with an age-structured HIV model with antiretrowviral therapy and two infection routes (virus-to-cell and cell-to-cell). The model is first formulated as an abstract non-densely defined Cauchy problem and the existence of the equilibria is obtained under some conditions. Based on the existence of equilibria, the global asymptotical stability of the disease-free equilibrium is studied by applying theory of operator semigroups and spectral analysis. The stability and Hopf bifurcation results with two delays around the endemic equilibrium are also well described under some conditions by the geometric stability switch criteria. Finally some numerical examples are presented to illustrate the obtained results.

KW - C-semigroup

KW - Hopf bifurcation

KW - age-structured HIV model

KW - asymptotical stability

KW - time delays

UR - https://www.scopus.com/pages/publications/105040015463

U2 - 10.1093/imamat/hxag008

DO - 10.1093/imamat/hxag008

M3 - 文章

AN - SCOPUS:105040015463

SN - 0272-4960

VL - 91

SP - 86

EP - 117

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

IS - 1

ER -

Asymptotic dynamics for an age-structured HIV model with two delays

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