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Mathematical Biosciences and Engineering (MBE)
 

Mathematical analysis and dynamic active subspaces for a long term model of HIV
Pages: 709 - 733, Issue 3, June 2017

doi:10.3934/mbe.2017040      Abstract        References        Full text (2764.9K)           Related Articles

Tyson Loudon - School of Mathematics, University of Minnesota-Twin Cities, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, United States (email)
Stephen Pankavich - Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401, United States (email)

1 D. Callaway and A. Perelson, HIV-1 infection and low steady state viral loads, Bull. Math.Biol., 64 (2002), 29-64.
2 P. Constantine, Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies, SIAM, 2015.       
3 P. Constantine and D. Gleich, Computing active subspaces with monte carlo, arXiv: 1408.0545
4 P. Constantine, B. Zaharatos and M. Campanelli, Discovering an active subspace in a single-diode solar cell model, Statistical Analysis and Data Mining: The ASA Data Science Journal, 8 (2015), 264-273.       
5 A. S. Fauci, G. Pantaleo, S. Stanley and et al., Immunopathogenic mechanisms of HIV infection, Annals of Internal Medicine, 124 (1996), 654-663.
6 T. C. Greenough, D. B. Brettler, F. Kirchhoff and et al., Long-term non-progressive infection with Human Immunodeficiency Virus in a Hemophilia cohort, J Infect Dis, 180 (1999), 1790-1802.
7 A. B. Gumel, P. N. Shivakumar and B. M. Sahai, A mathematical model for the dynamics of HIV-1 during the typical course of infection, Nonlinear Analysis, 47 (2001), 1773-1783.       
8 M. Hadjiandreou, R. Conejeros and V. S. Vassiliadis, Towards a long-term model construction for the dynamic simulation of HIV infection, Mathematical Biosciences and Engineering, 4 (2007), 489-504.
9 E. Hernandez-Vargas and R. Middleton, Modeling the three stages in HIV infection, J Theor Biol., 320 (2013), 33-40.       
10 T. Igarashi, C. R. Brown, Y. Endo and et al., Macrophages are the principal reservoir and sustain high virus loads in Rhesus Macaques following the depletion of CD4+ T-cells by a highly pathogenic SIV: Implications for HIV-1 infections of man, Proc Natl Acad Sci., 98 (2001), 658-663.
11 E. Jones and P. Roemer (sponsors: S. Pankavich and M. Raghupathi), Analysis and simulation of the three-component model of HIV dynamics, SIAM Undergraduate Research Online, 7 (2014), 89-106.
12 D. Kirschner, Using mathematics to understand HIV immunodynamics, Am. Math. Soc., 43 (1996), 191-202.       
13 D. E. Kirschner and A. S. Perelson, A model for the immune response to HIV: AZT treatment studies, Mathematical Population Dynamics: Analysis of Heterogeneity, Volume One: Theory of Epidemics Eds. O. Arino, D. Axelrod, M. Kimmel, and M. Langlais, Wuerz Publishing Ltd., Winnipeg, Canada, (1993), 295-310.
14 D. Kirschner and G. F. Webb, Immunotherapy of HIV-1 infection, J Biological Systems, 6 (1998), 71-83.
15 D. Kirschner, G. F. Webb and M. Cloyd, A model of HIV-1 disease progression based on virus-induced lymph node homing-induced apoptosis of CD4+ lymphocytes, J Acquir Immune Dec Syndr, 24 (2000), 352-362.
16 J. M. Murray, G. Kaufmann, A. D. Kelleher and et al., A model of primary HIV-1 infection, Math Biosci, 154 (1998), 57-85.
17 M. Nowak and R. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, NewYork, 2000.       
18 S. Pankavich, The effects of latent infection on the dynamics of HIV, Differential Equations and Dynamical Systems, 24 (2016), 281-303.       
19 S. Pankavich and D. Shutt, An in-host model of HIV incorporating latent infection and viral mutation, Dynamical Systems, Differential Equations, and Applications, AIMS Proceedings, (2015), 913-922.       
20 S. Pankavich, N. Neri and D. Shutt, Bistable dynamics and Hopf bifurcation in a refined model of the acute stage of HIV infection, submitted, (2015).
21 S. Pankavich and C. Parkinson, Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity, Discrete and Continuous Dynamical Systems B, 21 (2016), 1237-1257.       
22 E. Pennisi and J. Cohen, Eradicating HIV from a patient: Not just a dream?, Science, 272 (1996), 1884.
23 A. S. Perelson, Modeling the Interaction of the Immune System with HIV, Lecture Notes in Biomath. Berlin: Springer, 1989.       
24 A. Perelson and P. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.       
25 T. M. Russi, Uncertainty Quantification with Experimental data and Complex System Models, Ph.D. thesis, UC Berkeley, 2010.       
26 W. Y. Tan and H. Wu, Stochastic modeing of the dynamics of CD4+ T-cell infection by HIV and some monte carlo studies, Math Biosci, 147 (1997), 173-205.       
27 E. Vergu, A. Mallet and J. Golmard, A modeling approach to the impact of HIV mutations on the immune system, Comput Biol Med., 35 (2005), 1-24.

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