Dynamics of an HBV/HCV infection model with intracellular delay and cell proliferation

• An HBV/HCV model with intracellular delay and cell proliferation is analyzed.
• Pontryagin’s method is employed to derive sharp conditions ensuring stability of the infection persistent equilibrium.
• An alternative geometric stability switch criterion is proposed, which is used to show that the intracellular delay can induce stability switches.
• Numerical simulations reveal that the intracellular delay can induce chaos and interesting structure of bifurcation diagram exhibiting persistence bubbles.

A new mathematical model of hepatitis B/C virus (HBV/HCV) infection which incorporates the proliferation of healthy hepatocyte cells and the latent period of infected hepatocyte cells is proposed and studied. The dynamics is analyzed via Pontryagin’s method and a newly proposed alternative geometric stability switch criterion. Sharp conditions ensuring stability of the infection persistent equilibrium are derived by applying Pontryagin’s method. Using the intracellular delay as the bifurcation parameter and applying an alternative geometric stability switch criterion, we show that the HBV/HCV infection model undergoes stability switches. Furthermore, numerical simulations illustrate that the intracellular delay can induce complex dynamics such as persistence bubbles and chaos.