Mathematical analysis of a multiscale hepatitis C virus infection model with two viral strains

Abstract

Direct-acting antiviral agents (DAAs) have shown higher cure rates for treating hepatitis C virus (HCV) by directly interfering with different steps of the HCV life cycle. To optimize drug combinations and accurately quantify the antiviral effect of DAAs treatments, mathematical models should include the intracellular virus replication processes. In this study, we develop a two-strain multiscale age-structured model that includes intracellular viral RNA replication and extracellular viral infection. We prove the existence, positivity, and boundedness of the solution, and derive the conditions for the existence and stability of the three steady states (non-infection steady state, boundary steady state, and coexistence steady state). Under certain biologically reasonable assumptions, we obtain the approximate solutions of the viral load decline of the two virus strains (sensitive and drug-resistant virus strains) during treatment, and the long-term approximation is shown to be in good agreement with the solution of the original model. We also carry out numerical simulations using the long-term approximate solution, providing insights into the influence of antiviral effects on the viral load change of the two virus strains during treatment with DAAs.