  We examine two models for hepatitis C viral (HCV) dynamics, one for
monotherapy with interferon (IFN) and the other for combination therapy with
IFN and ribavirin. Optimal therapy for both the models is determined using the
steepest gradient method, by defining an objective functional which minimizes
the infected hepatocyte levels, virion population and the side-effects of the
drug(s). The optimal therapy for both the models shows an initial period of
high efficacy, followed by a gradual decline. The period of high efficacy
coincides with a significant decrease in the infected hepatocyte levels as well
as viral load, whereas the efficacy drops after liver regeneration through
restored hepatocyte levels. The period of high efficacy is not altered
significantly when the cost coefficients are varied, as long as the side
effects are relatively small. This suggests a higher dependence of the optimal
therapy on the model parameters in case of drugs with minimal side effects.
  We use the Latin hypercube sampling technique to randomly generate a large
number of patient scenarios (i.e, model parameter sets) and study the dynamics
of each set under the optimal therapy already determined. Results show an
increase in the percentage of responders (as indicated by drop in viral load
below detection levels) in case of combination therapy as compared to
monotherapy. Statistical tests performed to study the correlations between
sample parameters and the time required for the viral load to fall below
detection level, show a strong monotonic correlation with the death rate of
infected hepatocytes, identifying it to be an important factor in deciding
individual drug regimens.
