Global stability analysis of a nested multiscale model for intracellular and intercellular dynamics

Multiscale modeling is an important tool for the study of complex systems; it helps us gain a deeper understanding of the overall behavior of a system by integrating dynamic processes at different scales. In this paper, based on whether the hepatitis B virus (HBV) is infectious in the cell, we propose a staged progression nested multiscale model by coupling the intracellular and intercellular scales of the disease system. We derive the basic reproduction number $\mathcal{R}_{0}$ and the immune response reproduction number $\mathcal{R}_{1}$ for this multiscale model. By constructing three Lyapunov functions and using the Lasalle invariance principle, the global stability of the infection-free steady state is proved when $\mathcal{R}_{0}<1$ . When $\mathcal{R}_{1}<1<\mathcal{R}_{0}$ , sufficient conditions are derived for the global stability of the immune-free steady state. And when $\mathcal{R}_{0}>\mathcal{R}_{1}>1$ , sufficient conditions are derived for the global stability of the endemic steady state. Numerical results show that the proliferation of cytotoxic T lymphocytes (CTLs) can effectively reduce the concentration of infected cells. Interferon can directly inhibit the production of mature viral particles but has a limited effect on the formation of core particles. Additionally, reducing the conversion of core particles to mature viral particles significantly decreases the concentration of infected cells. These findings suggest that intervention at the stage of mature viral particle production, or during viral core particle formation before envelope acquisition, may be more effective in minimizing cellular viral infection. This strategy holds significant potential for antiviral therapy and offers a promising direction for the development of novel therapeutic approaches.