Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment

Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment

We investigate the dynamical behavior of a delayed HIV infection model with general incidence rate and immune impairment. We derive two threshold parameters, the basic reproduction number R0 and the immune response reproduction number R1. By using Lyapunov functional and LaSalle invariance principle...

Full description

Bibliographic Details
Main Authors: Fuxiang Li, Wanbiao Ma, Zhichao Jiang, Dan Li
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Computational and Mathematical Methods in Medicine
Online Access:http://dx.doi.org/10.1155/2015/206205
id doaj-b248f1b590d548f9b80088bf0136997a
record_format Article
spelling doaj-b248f1b590d548f9b80088bf0136997a2020-11-24T21:41:17ZengHindawi LimitedComputational and Mathematical Methods in Medicine1748-670X1748-67182015-01-01201510.1155/2015/206205206205Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune ImpairmentFuxiang Li0Wanbiao Ma1Zhichao Jiang2Dan Li3Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaDepartment of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaFundamental Science Department, North China Institute of Aerospace Engineering, Langfang, Hebei 065000, ChinaDepartment of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaWe investigate the dynamical behavior of a delayed HIV infection model with general incidence rate and immune impairment. We derive two threshold parameters, the basic reproduction number R0 and the immune response reproduction number R1. By using Lyapunov functional and LaSalle invariance principle, we prove the global stability of the infection-free equilibrium and the infected equilibrium without immunity. Furthermore, the existence of Hopf bifurcations at the infected equilibrium with CTL response is also studied. By theoretical analysis and numerical simulations, the effect of the immune impairment rate on the stability of the infected equilibrium with CTL response has been studied.http://dx.doi.org/10.1155/2015/206205
collection DOAJ
language English
format Article
sources DOAJ
author Fuxiang Li
Wanbiao Ma
Zhichao Jiang
Dan Li
spellingShingle Fuxiang Li
Wanbiao Ma
Zhichao Jiang
Dan Li
Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment
Computational and Mathematical Methods in Medicine
author_facet Fuxiang Li
Wanbiao Ma
Zhichao Jiang
Dan Li
author_sort Fuxiang Li
title Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment
title_short Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment
title_full Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment
title_fullStr Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment
title_full_unstemmed Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment
title_sort stability and hopf bifurcation in a delayed hiv infection model with general incidence rate and immune impairment
publisher Hindawi Limited
series Computational and Mathematical Methods in Medicine
issn 1748-670X
1748-6718
publishDate 2015-01-01
description We investigate the dynamical behavior of a delayed HIV infection model with general incidence rate and immune impairment. We derive two threshold parameters, the basic reproduction number R0 and the immune response reproduction number R1. By using Lyapunov functional and LaSalle invariance principle, we prove the global stability of the infection-free equilibrium and the infected equilibrium without immunity. Furthermore, the existence of Hopf bifurcations at the infected equilibrium with CTL response is also studied. By theoretical analysis and numerical simulations, the effect of the immune impairment rate on the stability of the infected equilibrium with CTL response has been studied.
url http://dx.doi.org/10.1155/2015/206205
work_keys_str_mv AT fuxiangli stabilityandhopfbifurcationinadelayedhivinfectionmodelwithgeneralincidencerateandimmuneimpairment
AT wanbiaoma stabilityandhopfbifurcationinadelayedhivinfectionmodelwithgeneralincidencerateandimmuneimpairment
AT zhichaojiang stabilityandhopfbifurcationinadelayedhivinfectionmodelwithgeneralincidencerateandimmuneimpairment
AT danli stabilityandhopfbifurcationinadelayedhivinfectionmodelwithgeneralincidencerateandimmuneimpairment
_version_ 1725922839836491776

Similar Items