Evaluating the Effect of Implementing Biologically Realistic Delays on Hepatitis C Kinetics and Associated Estimates of Antiviral Efficacy

Mathematical modelling of hepatitis C virus (HCV) decay under antiviral therapy has allowed for the determination of antiviral efficacy and other important parameters. Cur-rent models of HCV infection are based on a set of ordinary differential equations (ODEs)and assume that infectious cell lifespans are exponentially distributed over time, meaning that every infected cell has an equal probability of dying at any time. Here, we introduce a new model which: (1) allows for a realistic eclipse phase delay between the moment of cell infection and the release of new virus; and (2) considers both exponential and gamma-distributed delays for the time spent by cells in the infectious state, continuously producing virus. To allow for the simplest mathematical form, we consider a multiple-stage ODE model which yields gamma-distributed delays. Application of this model to viral titer data for patients undergoing antiviral therapy leads to different conclusions when predicting parameter values.