Abstract
Dynamical behaviors of an HBV infection model with distributed delay are studied. The model includes the ordinary, discrete delay and Gamma distributed delay differential equation models as special cases. The model always has two equilibria: the liver failure equilibrium which is unstable and the infection-free equilibrium which is globally asymptotically stable if the basic reproduction number \(R_{0}\leqslant 1\). There is an immune-free equilibrium if \(R_{0}>1\) and an endemic equilibrium if the CTL immune response reproduction number \(R_{1}>1\). We study the stability of these two equilibria in three models respectively. In the ODE model, they are globally asymptotically stable under some conditions. However, there are Hopf bifurcations near the equilibria in both delay models by using the (average) delay as a bifurcation parameter. Numerical simulations have been done to support the analytical findings.
Published Version
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