The dynamics of HIV models with switching parameters and pulse control

Xiying Wang; Xinzhi Liu; Wei Xu; Wei Chau Xie; Wanping Liu

doi:10.1142/S0218339016500200

The dynamics of HIV models with switching parameters and pulse control

Xiying Wang, Xinzhi Liu, Wei Xu, Wei Chau Xie, Wanping Liu

School of Mathematics and Statistics

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

3 Scopus citations

Abstract

This paper studies some human immunodeficiency virus (HIV) models with switching parameters and pulse control. The classical virus dynamics model is first modified by incorporating switching parameters which are assumed to be time-varying. Some threshold conditions are derived to guarantee the virus elimination by utilizing a Razumikhin-type approach. The results show that the proper switching conditions chosen can increase the counts of CD4⁺ T-cells while reducing viral load. Pulse control strategies are then applied to the above model. More precisely, the treatment strategy and the vaccination strategy are applied to infected cells and uninfected cells, respectively. Each control strategy is analyzed to gauge its success in achieving viral suppression. Numerical simulations are performed to complement the analytical results and motivate future directions.

Original language	English
Pages (from-to)	385-407
Number of pages	23
Journal	Journal of Biological Systems
Volume	24
Issue number	4
DOIs	https://doi.org/10.1142/S0218339016500200
State	Published - 1 Dec 2016

Keywords

Basic Reproduction Number
HIV Model
Pulse Control Schemes
Stability
Switched System

UN SDGs

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

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10.1142/S0218339016500200

Cite this

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title = "The dynamics of HIV models with switching parameters and pulse control",

abstract = "This paper studies some human immunodeficiency virus (HIV) models with switching parameters and pulse control. The classical virus dynamics model is first modified by incorporating switching parameters which are assumed to be time-varying. Some threshold conditions are derived to guarantee the virus elimination by utilizing a Razumikhin-type approach. The results show that the proper switching conditions chosen can increase the counts of CD4+ T-cells while reducing viral load. Pulse control strategies are then applied to the above model. More precisely, the treatment strategy and the vaccination strategy are applied to infected cells and uninfected cells, respectively. Each control strategy is analyzed to gauge its success in achieving viral suppression. Numerical simulations are performed to complement the analytical results and motivate future directions.",

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T1 - The dynamics of HIV models with switching parameters and pulse control

AU - Wang, Xiying

AU - Liu, Xinzhi

AU - Xu, Wei

AU - Xie, Wei Chau

AU - Liu, Wanping

PY - 2016/12/1

Y1 - 2016/12/1

N2 - This paper studies some human immunodeficiency virus (HIV) models with switching parameters and pulse control. The classical virus dynamics model is first modified by incorporating switching parameters which are assumed to be time-varying. Some threshold conditions are derived to guarantee the virus elimination by utilizing a Razumikhin-type approach. The results show that the proper switching conditions chosen can increase the counts of CD4+ T-cells while reducing viral load. Pulse control strategies are then applied to the above model. More precisely, the treatment strategy and the vaccination strategy are applied to infected cells and uninfected cells, respectively. Each control strategy is analyzed to gauge its success in achieving viral suppression. Numerical simulations are performed to complement the analytical results and motivate future directions.

AB - This paper studies some human immunodeficiency virus (HIV) models with switching parameters and pulse control. The classical virus dynamics model is first modified by incorporating switching parameters which are assumed to be time-varying. Some threshold conditions are derived to guarantee the virus elimination by utilizing a Razumikhin-type approach. The results show that the proper switching conditions chosen can increase the counts of CD4+ T-cells while reducing viral load. Pulse control strategies are then applied to the above model. More precisely, the treatment strategy and the vaccination strategy are applied to infected cells and uninfected cells, respectively. Each control strategy is analyzed to gauge its success in achieving viral suppression. Numerical simulations are performed to complement the analytical results and motivate future directions.

KW - Basic Reproduction Number

KW - HIV Model

KW - Pulse Control Schemes

KW - Stability

KW - Switched System

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The dynamics of HIV models with switching parameters and pulse control

Abstract

Keywords

UN SDGs

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