Sensitivity analysis of a nonlinear lumped parameter model of HIV infection dynamics

A formal sensitivity analysis is performed on a delay differential equation model for the viral dynamics of an in vivo HIV infection during protease inhibitor therapy. We present results of both a differential analysis as well as a principle component based analysis and provide evidence that suggests the exact times at which specific parameters have the most influence over the solution. We offer insight into the pairwise mathematical relationships between the productively infected T-cell death rate delta, the viral plasma clearance rate c, and the time delay tau between infection and viral production as they relate to the viral dynamics. The results support the claim that the presence of a nonzero delay has a major impact on the model dynamics. Lastly, we comment upon the inadequacies of an alternative principle component based analysis.