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.
We consider a mathematical model comprising of four coupled ordinary differential equations (ODEs) for studying the hepatitis C (HCV) viral dynamics. The model embodies the efficacies of a combination therapy of interferon and ribavirin. A condition
for the stability of the uninfected and the infected steady states is presented. A large number of sample points for the model parameters (which were physiologically feasible) were generated using Latin hypercube sampling. Analysis of our simulated values indicated approximately 24% cases as having an uninfected steady state. Statistical tests like the chi-square-test and the Spearmans test were also done on the sample values. The results of these tests indicate a distinctly differently distribution of certain parameter values and not in case of others, vis-a-vis, the stability of the uninfected and the infected steady states.
