1 |
B. M. Adams, H. T. Banks, M. Davidian, H. D. Kwon, H. T. Tran, S. N. Wynne, and E. S. Rosenberg, HIV dynamics: Modeling, data analysis, and optimal treatment protocols, J. Comput. Appl. Math. 184 (2005), no. 1, 10-49.
DOI
ScienceOn
|
2 |
B. M. Adams, H. T. Banks, H. D. Kwon, and H. T. Tran, Dynamic multidrug therapies for HIV: Optimal and STI control approaches, Math. Biosci. Eng. I (2004), no. 2, 223-241.
|
3 |
J. Alvarez-Ramirez, M. Meraz, and J. X. Velasco-Hernandez, Feedback control of the chemotherapy of HIV, Int. J. Bifur. Chaos 10 (2000), 2207-2219.
|
4 |
H. T. Banks, H. D. Kwon, J. A. Toivanen, and H. T. Tran, A state-dependent Riccati equation-based estimator approach for HIV feedback control, Optimal Control Appl. Methods 27 (2006), no. 2, 93-121.
DOI
ScienceOn
|
5 |
S. Bonhoeffer, M. Rembiszewski, G. M. Ortiz, and D. F. Nixon, Risks and benefits of structured antiretroviral drug therapy interruptions in HIV-1 infection, AIDS 14 (2000), 2313-2322.
DOI
ScienceOn
|
6 |
M. E. Brandt and G. Chen, Feedback control of a biodynamical model of HIV-1, IEEE Trans. on Biom. Engrg. 48 (2001), 754-759.
DOI
ScienceOn
|
7 |
D. S. Callaway and A. S. Perelson, HIV-1 infection and low steady state viral loads, Bull. Math. Biol. 64 (2001), 29-64.
|
8 |
A. Carr and D. A. Cooper, Adverse effects of antiretroviral therapy, Lancet 356 (2000), 1423-1430.
DOI
ScienceOn
|
9 |
Y. H. Dai, L. Z. Liao, and D. Li, On restart procedures for the conjugate gradient method, Numer. Algorithms 35 (2004), no. 2-4, 249-260.
DOI
|
10 |
K. R. Fister, S. Lenhart, and J. S. McNally, Optimizing chemotherapy in an HIV model, Electron. J. Differential Equation 1998 (1998), no. 32, 1-12.
|
11 |
W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag, New York, 1975.
|
12 |
J. C. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim. 2 (1992), no. 1, 21-42.
DOI
|
13 |
B. Julg and F. D. Goebel, Treatment interruption in HIV therapy: A SMART Strategy?, Infection 34 (2006), 186-288.
DOI
|
14 |
D. Kirschner, S. Lenhart, and S. Serbin, Optimal control of the chemotherapy of HIV, J. Math. Bio. 35 (1997), no. 7, 775-792.
DOI
|
15 |
L. S. Lasdon, S. K. Mitter, and A. D. Waren, The conjugate gradient method for optimal control problems, IEEE Trans. Automatic Control AC-12 (1967), no. 2, 132-138.
|
16 |
J. Lisziewicz and F. Lori, Structured treatment interruptions in HIV/AIDS therapy, Microbes and Infection 4 (2002), 207-214.
DOI
ScienceOn
|
17 |
F. Lori, R. Maserati, et al., Structured treatment interruptions to control HIV-1 infection, The Lancet 354 (2000), 287-288.
|
18 |
G. C. Palacios, L. M. Sanchez, E. Briones, T. J. Ramirez, H. Castillo, L. G. Rivera, C. A. Vazquez, C. Rodriguez-Padilla, and M. Holodniy, Structured interruptions of highly active antiretroviral therapy in cycles of 4 weeks off/12 weeks on therapy in children having a chronically undetectable viral load cause progressively smaller viral rebounds, Int. J. Infect. Dis. 14 (2010), e34-e40.
|
19 |
D. L. Lukes, Differential Equations: Classical to Controlled, Mathematics in Science and Engineering, Academic Press, New York, 1982.
|
20 |
E. L. Murphy, A. C. Collier, L. A. Kalish, S. F. Assmann, M. F. Para, T. P. Flanigan, P. N. Kumar, L. Mintz, R. R. Wallach, and G. J. Nemo, Highly active antiretroviral therapy decreases mortality and morbidity in patients with advanced HIV disease, Ann. Intern. Med. 135 (2001), 17-26.
DOI
ScienceOn
|
21 |
F. J. Palella Jr, K. M. Delaney, A. C. Moorman, M. O. Loveless, J. Fuhrer, G. A. Satten, D. J. Aschman, S. D. Holmberg, Declining morbidity and mortality among patients with advanced human immunodeficiency virus infection, HIV Putpatient Study Investigators, N. Engl. J. Med. 338 (1998), 853-860.
DOI
ScienceOn
|
22 |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Interscience Publishers John Wiley and Sons, Inc. 528, New York-London, 28, 1962.
|
23 |
E. S. Rosenberg, M. Davidian, and H. T. Banks, Using mathematical modeling andcontrol to develop structured treatment interruption strategies for HIV infection, Drugand Alcohol Dependence 88S (2007), S41-S51.
|
24 |
Z. J. Shi and J. Guo, A new algorithm of nonlinear conjugate gradient method with strong convergence, Comput. Appl. Math. 27 (2008), no. 1, 93-106.
|
25 |
S. Tang, Y. Xiao, N. Wang, and H. Wu, Piecewise HIV virus dynamic model with CD4+T cell count-guided therapy: I, J. Theoret. Biol. 308 (2012), 123-134.
DOI
ScienceOn
|
26 |
H. Shim, S. J. Han, C. C. Chung, S. Nam, and J. H. Seo, Optimal scheduling of drug treatment for HIV infection: Continuous dose control and receding horixon control, Int. J. Control Autom. Systems 1 (2003), 401-407.
|
27 |
J. D. Siliciano, J. Kajdas, D. Finzi, T. C. Quinn, K. Chadwick, J. B. Margolick, C. Kovacs, S. J. Gange, and R. F. Siliciano, Long-term follow-up studies confirm the stability of the latent reservoir for HIV-1 in resting CD4+ T cells, Nat. Med. 9 (2003), 727-728.
DOI
ScienceOn
|
28 |
H. M. Speigel, et al., Changes in frequency of HIV-1 specific cytotoxic T cell precursors and circulating effectors after combination anti-retroviral therapy in children, J. Inf. Dis. 180 (1999), 359-368.
DOI
ScienceOn
|
29 |
L. M. Wein, S. A. Zenios, and M. A. Nowak, Dynamic multidrug therapies for HIV: A control theoretic approach, J. Theoret. Biol. 185 (1997), 15-29.
DOI
ScienceOn
|
30 |
D. Wodarz and M. A. Nowak, Specific therapy regimes could lead to long-term immunological control of HIV, Proceedings of the National Academy of Sciences 96 (1999), 4464-14469.
|