Global stability and periodic solution of the viral dynamics

Xinyu Song; Avidan U. Neumann

doi:10.1016/j.jmaa.2006.06.064

Global stability and periodic solution of the viral dynamics

Xinyu Song, Avidan U. Neumann

The Mina and Everard Goodman Faculty of Life Sciences - at Bar-Ilan University

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

211 Scopus citations

Abstract

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

Original language	English
Pages (from-to)	281-297
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	329
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2006.06.064
State	Published - 1 May 2007

Bibliographical note

Funding Information:
✩ This work is supported by the National Natural Science Foundation of China (No. 10471117), the Henan Innovation Project for University Prominent Research Talents (No. 2005KYCX017) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. * Corresponding author. E-mail address: [email protected] (X. Song).

Funding

✩ This work is supported by the National Natural Science Foundation of China (No. 10471117), the Henan Innovation Project for University Prominent Research Talents (No. 2005KYCX017) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. * Corresponding author. E-mail address: [email protected] (X. Song).

Funders	Funder number
Henan Innovation Project for University Prominent Research Talents	2005KYCX017
State Education Ministry
National Natural Science Foundation of China	10471117
Scientific Research Foundation for Returned Scholars of Ministry of Education

Keywords

Global stability
HIV, HBV and HCV
Periodic solution

UN SDGs

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

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10.1016/j.jmaa.2006.06.064

Cite this

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title = "Global stability and periodic solution of the viral dynamics",

abstract = "It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.",

keywords = "Global stability, HIV, HBV and HCV, Periodic solution",

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N2 - It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

AB - It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

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Global stability and periodic solution of the viral dynamics

Abstract

Bibliographical note

Funding

Keywords

UN SDGs

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