Mathematical analysis and dynamic active subspaces for a long term model of HIV
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 s...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2017-05-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017040 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590065004445696 |
|---|---|
| author | Tyson Loudon Stephen Pankavich |
| author_facet | Tyson Loudon Stephen Pankavich |
| author_sort | Tyson Loudon |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8c6c95fbe75744de8a0cf8b952ae5671 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-8c6c95fbe75744de8a0cf8b952ae56712025-01-24T02:39:47ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-05-0114370973310.3934/mbe.2017040Mathematical analysis and dynamic active subspaces for a long term model of HIVTyson Loudon0Stephen Pankavich1School of Mathematics, University of Minnesota-Twin Cities, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, USADepartment of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, USARecently, 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.https://www.aimspress.com/article/doi/10.3934/mbe.2017040hiv modelingstability analysisactive subspacesdimension reductionsensitivity analysis |
| spellingShingle | Tyson Loudon Stephen Pankavich Mathematical analysis and dynamic active subspaces for a long term model of HIV Mathematical Biosciences and Engineering hiv modeling stability analysis active subspaces dimension reduction sensitivity analysis |
| title | Mathematical analysis and dynamic active subspaces for a long term model of HIV |
| title_full | Mathematical analysis and dynamic active subspaces for a long term model of HIV |
| title_fullStr | Mathematical analysis and dynamic active subspaces for a long term model of HIV |
| title_full_unstemmed | Mathematical analysis and dynamic active subspaces for a long term model of HIV |
| title_short | Mathematical analysis and dynamic active subspaces for a long term model of HIV |
| title_sort | mathematical analysis and dynamic active subspaces for a long term model of hiv |
| topic | hiv modeling stability analysis active subspaces dimension reduction sensitivity analysis |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017040 |
| work_keys_str_mv | AT tysonloudon mathematicalanalysisanddynamicactivesubspacesforalongtermmodelofhiv AT stephenpankavich mathematicalanalysisanddynamicactivesubspacesforalongtermmodelofhiv |