  Recently, a long-term model of HIV infection dynamics was developed to
describe the entire time course of the disease. It consists of a large system
of ODEs with many parameters, and is expensive to simulate. In the current
paper, this model is analyzed by determining all infection-free steady states
and studying the local stability properties of the unique biologically-relevant
equilibrium. Active subspace methods are then used to perform a global
sensitivity analysis and study the dependence of an infected individual's
T-cell count on the parameter space. Building on these results, a
global-in-time approximation of the T-cell count is created by constructing
dynamic active subspaces and reduced order models are generated, thereby
allowing for inexpensive computation.
