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

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Abstract

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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Authors and Affiliations

  1. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210046, P.R. China

    Jianhua Pang

  2. Department of Information and Computing, Guangxi University of Technology, Liuzhou, 545006, P.R. China

    Jianhua Pang

  3. School of Science, Beijing University of Civil Engineering and Architecture, Beijing, 100044, P.R. China

    Jing-an Cui

  4. Mechanical Engineering Department, Guangxi University of Technology, Liuzhou, 545006, P.R. China

    Jing Hui

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  1. Jianhua Pang
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  2. Jing-an Cui
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Correspondence to Jing-an Cui.

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Pang, J., Cui, Ja. & Hui, J. The importance of immune responses in a model of hepatitis B virus. Nonlinear Dyn 67, 723–734 (2012). https://doi.org/10.1007/s11071-011-0022-6

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  • DOI: https://doi.org/10.1007/s11071-011-0022-6

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