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The importance of immune responses in a model of hepatitis B virus. (English) Zbl 1242.92042
Summary: The dynamical behavior of a hepatitis B virus model with cytotoxix T-lymphociye (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 response play a significant and decisive role in the eradication of the disease. The study and information derived from this model may have an important impact on treatment protocols of the hepatitis B virus in the future.
MSC:
92C60Medical epidemiology
34C60Qualitative investigation and simulation of models (ODE)
34D20Stability of ODE
65C20Models (numerical methods)
References:
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