Global stability and optimal control of an HBV/HCV coinfection model with humoral immunity and cell-to-cell transmission

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Abstract

In this study, we investigate the dynamics of a within-host model of hepatitis B virus (HBV) and hepatitis C virus (HCV) coinfection with two distinct transmission pathways: virus-to-cell and cell-to-cell transmission. The model incorporates both HBV-specific and HCV-specific humoral immunity. Using the next-generation matrix method, we derive the basic reproduction numbers for HBV mono-infection ($\mathcal{R}_{0}^{B}$), HCV mono-infection ($\mathcal{R}_{0}^{C}$), and HBV/HCV coinfection ($\mathcal{R}_{0}$ = max{$\mathcal{R}_{0}^{B}$, $\mathcal{R}_{0}^{C}$}). We establish the fundamental qualitative properties of the model, identify eight possible equilibrium points, and investigate their global stability. The stability analysis is carried out using Lyapunov functions together with the Lyapunov–LaSalle invariance principle. The model is further formulated as a nonlinear control system, where anti-HBV and anti-HCV therapies serve as the control inputs. For each virus, two antiviral treatment strategies are considered: one that reduces virus-to-cell transmission and another that reduces cell-to-cell transmission. The results show that neglecting cell-to-cell transmission may underestimate the treatment effort required for viral clearance, highlighting the importance of incorporating this transmission pathway to obtain more realistic descriptions of within-host HBV/HCV dynamics. The optimal control problem is formulated to maximize the population of uninfected hepatocytes while minimizing treatment costs. Numerical simulations illustrate the theoretical results and demonstrate that the proposed control strategies can reduce viral infections and increase the population of uninfected hepatocytes under the considered parameter scenarios. Finally, sensitivity analysis of $\mathcal{R}_{0}^{B}$ and $\mathcal{R}_{0}^{C}$ identifies the parameters that have the greatest influence on the basic reproduction numbers, providing insights into the model mechanisms associated with viral persistence and clearance.

Keywords

hepatitis B virus / hepatitis C virus / global stability / Lyapunov function / optimal control

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