Dynamics of hepatitis C under optimal therapy and sampling based analysis

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 infected hepatocyte levels, virion population and side-effects of the drug(s). The optimal therapies for both the models show an initial period of high efficacy, followed by a gradual decline. The period of high efficacy coincides with a significant decrease in the viral load, whereas the efficacy drops after hepatocyte levels are restored. the Latin hypercube sampling technique to randomly generate a large number of patient scenarios and study the dynamics of each set under the optimal therapy already determined. Results show an increase in the percentage of responders (indicated by drop in viral load below detection levels) in case of combination therapy (72%) as compared to monotherapy (57%). Statistical tests performed to study correlations between sample parameters and 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.