In this paper, we study an age-structured hepatitis B virus model with DNA-containing capsids. We obtain the well-posedness of the model by reformulate the model as an abstract Cauchy problem, and we find a threshold number \(\mathfrak {R}_0\) for the existence of the steady states. The local stability of each steady states is established by linearizing the system and analyze the corresponding characteristic equation. Furthermore, we investigate the uniform persistence of the system and constructing Lyapunov functionals to show the global stability of each steady states. We observe that the virus-free steady state is globally asymptotically stable when \(\mathfrak {R}_0<1\), while the infection steady state is globally asymptotically stable when \(\mathfrak {R}_0>1\). Numerical simulations are also presented to support the analytical results.

在本文中，我们研究了具有DNA衣壳的年龄结构的乙型肝炎病毒模型。通过将模型重新构造为抽象的柯西问题，我们获得了模型的适定性，并且找到了存在稳态的阈值\（\ mathfrak {R} _0 \）。通过线性化系统并分析相应的特征方程，可以建立每个稳态的局部稳定性。此外，我们研究了系统的一致持久性，并构造了Lyapunov函数以显示每个稳态的全局稳定性。我们观察到，当\（\ mathfrak {R} _0 <1 \）时，无病毒稳态是全局渐近稳定的，而当\（\ mathfrak {R} _0> 1 \）时，感染稳态是全局渐近稳定的。。还提供了数值模拟以支持分析结果。