A perspective on modelling hepatitis C virus infection

Abstract

By mathematically describing early hepatitis C virus (HCV) RNA decay after initiation of interferon (IFN)-based antiviral therapy, crucial parameters of the in vivo viral kinetics have been estimated, such as the rate of production and clearance of free virus, and the rate of loss of infected cells. Furthermore, by suggesting mechanisms of action for IFN and ribavirin mathematical modelling has provided a means for evaluating and optimizing treatment strategies. Here, we review recent modelling developments for understanding complex viral kinetics patterns, such as triphasic HCV RNA declines and viral rebounds observed in patients treated with pegylated interferon and ribavirin. Moreover, we discuss new modelling approaches developed to interpret the viral kinetics observed in clinical trials with direct-acting antiviral agents, which induce a rapid decline of wild-type virus but also engender a higher risk for emergence of drug-resistant variants. Lastly, as in vitro systems have allowed a better characterization of the virus lifecycle, we discuss new modelling approaches that combine the intracellular and the extracellular viral dynamics.

Figure 1

Schematic representation of the standard model (upper left), the extended model with cell proliferation (upper right) and the model with two strains of virus (bottom). The red and green X’s indicate steps in the viral lifecycle where IFN or DAAs interfere with virus production. The symbols are defined in the text.

Figure 2

Representative examples of viral kinetics patterns under treatment. HCV RNA digitalized data (circles) and their corresponding fits by the standard or extended model. Grey: biphasic responder with (daily) 10 MIU IFN (6) (ε=0.95, δ=0.16 d⁻¹, c=5.6 d⁻¹) (standard model); red: flat responder with (daily) 10 MIU IFN (70) (standard or extended model); blue: triphasic responder with (daily) 10 MIU IFN (6) (extended model); black: telaprevir plus (weekly) peg-IFNα-2a for 14 days (48) (ε=0.999, δ=0.5 d⁻¹, c=11 d⁻¹) (standard model); black dashed line: viral kinetics decline if the second phase viral decline was similar to what is observed with IFN (ε=0.999, δ=0.16 d⁻¹, c=11 d⁻¹).

Figure 3

Typical PK/PD viral kinetics profiles with weekly subcutaneous injections of 180 μg of peg-IFNα-2a (left) and 1.5μg/kg of peg-IFNα-2b (right); viral load (black) and serum peg-IFN concentration (green). The PK parameters have been obtained using median values given in (23) and the PD parameters are the median values for peg-IFNα-2a and a typical patient for peg-IFNα-2b in (21-22).

Figure 4

HCV RNA data (circles, patient 1002 in (42)) during telaprevir monotherapy (green is WT, red is RES) and best-fit of the two-strain viral kinetic model (42) (solid lines). The dashed grey line is the proportion of resistant virus V_RES/ (V_WT +V_RES).