2016/04/15 by Tyson Loudon, Loudon, Tyson, Stephen Pankavich +1 · 1 citation
Medicine · Mathematics · #Mathematical and Theoretical Epidemiology and Ecology Models #Fractional Differential Equations Solutions #COVID-19 epidemiological studies
paper · pdf · doi:10.48550/arxiv.1604.04588
Recently, a long-term model of HIV infection dynamics was developed to\ndescribe the entire time course of the disease. It consists of a large system\nof ODEs with many parameters, and is expensive to simulate. In the current\npaper, this model is analyzed by determining all infection-free steady states\nand studying the local stability properties of the unique biologically-relevant\nequilibrium. Active subspace methods are then used to perform a global\nsensitivity analysis and study the dependence of an infected individual's\nT-cell count on the parameter space. Building on these results, a\nglobal-in-time approximation of the T-cell count is created by constructing\ndynamic active subspaces and reduced order models are generated, thereby\nallowing for inexpensive computation.\n