Global Dynamics of a Virus-Immune System with Virus-Guided Therapy and Saturation Growth of Virus
We considered a piecewise virus-immune dynamic model to investigate the effectiveness of the HIV virus loads-guided structured treatment interruptions (STIs). To better describe the biological reality, we extended the existing models by taking the carrying capacity of the virus loads into considerat...
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2018/4710586 |
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doaj-a72a0c1d5b644014a0e5b2beef3833512020-11-24T23:40:06ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/47105864710586Global Dynamics of a Virus-Immune System with Virus-Guided Therapy and Saturation Growth of VirusQian Li0Yanni Xiao1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaWe considered a piecewise virus-immune dynamic model to investigate the effectiveness of the HIV virus loads-guided structured treatment interruptions (STIs). To better describe the biological reality, we extended the existing models by taking the carrying capacity of the virus loads into consideration to indicate the saturated growth of virus loads. We initially investigated the sliding dynamics of the proposed model and then obtained the global dynamics of the proposed model. Our main results showed that the system can exhibit very complex and diverse dynamic behaviors including a globally asymptotically stable equilibrium, bistable equilibra, and tristable equilibria, depending on the dynamics of the subsystems and the threshold level. In particular, an interesting result indicated that, with a proper threshold condition, the virus-guided therapy policy can successfully control the virus loads far below its carrying capacity and maintain the activity of the immune system for the case that the effector cells always go to zero without therapy or with continuous therapy. The finding suggested that the optimal strategy should be individual-based due to coexistence of multiple stable steady states, depending on the threshold conditions and the initial levels of viral loads and effector cells of the patients.http://dx.doi.org/10.1155/2018/4710586 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Qian Li Yanni Xiao |
spellingShingle |
Qian Li Yanni Xiao Global Dynamics of a Virus-Immune System with Virus-Guided Therapy and Saturation Growth of Virus Mathematical Problems in Engineering |
author_facet |
Qian Li Yanni Xiao |
author_sort |
Qian Li |
title |
Global Dynamics of a Virus-Immune System with Virus-Guided Therapy and Saturation Growth of Virus |
title_short |
Global Dynamics of a Virus-Immune System with Virus-Guided Therapy and Saturation Growth of Virus |
title_full |
Global Dynamics of a Virus-Immune System with Virus-Guided Therapy and Saturation Growth of Virus |
title_fullStr |
Global Dynamics of a Virus-Immune System with Virus-Guided Therapy and Saturation Growth of Virus |
title_full_unstemmed |
Global Dynamics of a Virus-Immune System with Virus-Guided Therapy and Saturation Growth of Virus |
title_sort |
global dynamics of a virus-immune system with virus-guided therapy and saturation growth of virus |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2018-01-01 |
description |
We considered a piecewise virus-immune dynamic model to investigate the effectiveness of the HIV virus loads-guided structured treatment interruptions (STIs). To better describe the biological reality, we extended the existing models by taking the carrying capacity of the virus loads into consideration to indicate the saturated growth of virus loads. We initially investigated the sliding dynamics of the proposed model and then obtained the global dynamics of the proposed model. Our main results showed that the system can exhibit very complex and diverse dynamic behaviors including a globally asymptotically stable equilibrium, bistable equilibra, and tristable equilibria, depending on the dynamics of the subsystems and the threshold level. In particular, an interesting result indicated that, with a proper threshold condition, the virus-guided therapy policy can successfully control the virus loads far below its carrying capacity and maintain the activity of the immune system for the case that the effector cells always go to zero without therapy or with continuous therapy. The finding suggested that the optimal strategy should be individual-based due to coexistence of multiple stable steady states, depending on the threshold conditions and the initial levels of viral loads and effector cells of the patients. |
url |
http://dx.doi.org/10.1155/2018/4710586 |
work_keys_str_mv |
AT qianli globaldynamicsofavirusimmunesystemwithvirusguidedtherapyandsaturationgrowthofvirus AT yannixiao globaldynamicsofavirusimmunesystemwithvirusguidedtherapyandsaturationgrowthofvirus |
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1725511046208159744 |