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

  • 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.

    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

    Related Papers:

  • 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.


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