Mathematical analysis and dynamic active subspaces for a long term model of HIV

Tyson Loudon; Stephen Pankavich; Tyson Loudon; Stephen Pankavich

doi:10.3934/mbe.2017040

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 3: 709-733. doi: 10.3934/mbe.2017040

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Mathematical analysis and dynamic active subspaces for a long term model of HIV

Tyson Loudon ¹,
Stephen Pankavich ^{2
,
,}

1.
School of Mathematics, University of Minnesota-Twin Cities, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, USA
2.
Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, USA

Received: 04 November 2015 Accepted: 23 October 2016 Published: 01 June 2017
MSC : Primary: 92B99; Secondary: 34A34

Recently, 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.
- HIV modeling,
- stability analysis,
- active subspaces,
- dimension reduction,
- sensitivity analysis
Citation: Tyson Loudon, Stephen Pankavich. Mathematical analysis and dynamic active subspaces for a long term model of HIV[J]. Mathematical Biosciences and Engineering, 2017, 14(3): 709-733. doi: 10.3934/mbe.2017040

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Abstract

Recently, 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.

References

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