The importance of immune responses in a model of hepatitis B virus

In this paper, the dynamical behavior of a hepatitis B virus model with CTL immune responses is studied. Analyzing the model, we show that the virus-free equilibrium is globally asymptotically stable if the basic reproductive ratio of virus is less than one and the endemic equilibrium is locally asy...

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Bibliographic Details
Published inNonlinear dynamics Vol. 67; no. 1; pp. 723 - 734
Main Authors Pang, Jianhua, Cui, Jing-an, Hui, Jing
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.01.2012
Springer Nature B.V
Subjects
Asymptotic properties
Automotive Engineering
Classical Mechanics
Computer simulation
Control
Dynamical Systems
Engineering
Hepatitis
Hepatitis B
Hepatitis B virus
Mathematical analysis
Mechanical Engineering
Original Paper
Vibration
Viruses
Basic reproductive ratio
Viral dynamics
Noncytolytic mechanisms
Cytolytic mechanisms
Permanence
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Summary:In this paper, the dynamical behavior of a hepatitis B virus model with CTL immune responses is studied. Analyzing the model, we show that the virus-free equilibrium is globally asymptotically stable if the basic reproductive ratio of virus is less than one and the endemic equilibrium is locally asymptotically stable if the basic reproductive ratio is greater than one. When the basic reproductive ratio is greater than one, the system is uniformly persistent, which means the virus is endemic. Mathematical analysis and numerical simulations show that the CTL immune responses play a significant and decisive role in eradication of disease. The study and information derived from this model may have an important impact on treatment protocols of hepatitis B virus in the future.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-011-0022-6