Analysis of Hepatitis C Viral Dynamics Using Latin Hypercube Sampling

TL;DR

This paper models hepatitis C viral dynamics with differential equations, using Latin hypercube sampling to analyze parameter effects on infection stability and employing statistical tests to interpret the results.

Contribution

It introduces a mathematical model for HCV dynamics incorporating therapy effects and applies Latin hypercube sampling for parameter analysis.

Findings

Approximately 24% of cases reach an uninfected steady state.

Parameter distributions differ significantly for stable and unstable states.

Statistical tests reveal key parameters influencing viral clearance.

Abstract

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 Spearman's 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.