title: Mathematical analysis and dynamic active subspaces for a long term model of HIV.
abstract: a long-term model of HIV infection dynamics [8] 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.
authors.affiliation: School of Mathematics, University of Minnesota-Twin Cities, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, United States . email: tloudon@umn.edu.
authors.forename: Tyson
authors.initials: T
authors.lastname: Loudon
authors.forename: Stephen
authors.initials: S
authors.lastname: Pankavich
mesh_terms: D002452:Cell Count; D004812:Epidemiologic Methods; D015658:HIV Infections / Q000453:epidemiology; D006801:Humans; D008954:Models, Biological; D013601:T-Lymphocytes / Q000166:cytology