Mathematical Modeling of HCV Viral Kinetics

Hepatitis C virus (HCV) is a single-stranded RNA virus that infects the hepatocytes of the liver. Infected cells become damaged and release alanine aminotransferase (ALT), which exists normally within liver cells. Our main goal in this project was to determine the usefullness of ALT levels to determine the outcome of HCV treatment and viral load levels. As part of our investigations, we first looked for correlations between ALT levels and viral load in order to examine the hypothesis that ALT levels could have the capability to estimate viral load. Since we did not have quantitative viral load data, we created a mathematical model and simulated data to test these correlations. Next, we created boxplots for each month of our simulated and collected ALT data to observe the differences in their distributions over time. This was also to determine whether or not our simulated data could be useful in drawing conclusions about how ALT levels and viral load are correlated in reality. The next objective was to use principal component analysis to identify the principal components responsible for the most significant portion of variation in the data. Finally, the simulated data was generated for different longitudinal schedules of observation to compare the parameter estimates and standard errors. By doing this, we were able to suggest alternative time points for which to collect data that would allow more efficient estimation of parameters in the future.