Optimal control for HIV multitherapy enhancement;Application du contrôle optimal à l'amélioration des trithérapies

Comptes Rendus Mathematique

Volumn 348, Issue 21-22, 2010, Pages 1179-1183

  Orellana, Jose Marie ^a  

^a University of Paris Cité   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78149499294     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2010.10.020     Document Type: Article

References (17)

1. Bonhoeffer S., Rembiszewski M., Ortiz G., Nixon D. Risks and benefits of structured antiretroviral drug therapy interruptions in HIV-1 infection. AIDS 2000, 14(15):2313.
2. Bryson A., Ho Y. Applied Optimal Control 1975, Wiley, New York.
3. Callaway D., Perelson A. HIV-1 infection and low steady state viral loads. Bulletin of Mathematical Biology 2002, 64(1):29-64.
4. Culshaw R., Ruan S. A delay-differential equation model of HIV infection of CD4+ T-cells. Mathematical Biosciences 2000, 165(1):27-39.
5. Culshaw R., Ruan S., Spiteri R. Optimal HIV treatment by maximising immune response. Journal of Mathematical Biology 2004, 48(5):545-562.
6. Ph. Destuynder, Analyse et contrôle des systèmes modélisés par des équations différentielles, Cours du CNAM Calcul Scientifique, Paris, 2008.
7. Dornadula G., et al. Residual HIV-1 RNA in blood plasma of patients taking suppressive highly active antiretroviral therapy. The Journal of the American Medical Association 1999, 282(17):1627-1632.
8. Garira W., Musekwa S., Shiri T. Optimal control of combined therapy in a single strain HIV-1 model. Electronic Journal of Differential Equations 2005, 52:1-22.
9. Fister K., Lenhart S., McNally J. Optimizing chemotherapy in an HIV model. Electronic Journal of Differential Equations 1998, 32:1-12.
10. Knorr A.L., Srivastava R. Evaluation of HIV-1 kinetic models using quantitative discrimination analysis. Bioinformatics 2005, 21(8):1668-1677.
11. Lewis F., Syrmos V. Optimal Control 1995, Wiley-Interscience.
12. Nowak M., Bonhoeffer S., Shaw G., May R. Anti-viral drug treatment: dynamics of resistance in free virus and infected cell populations. Journal of Theoretical Biology 1997, 184(2):203-217.
13. Orellana J. Optimal control for HIV therapy strategies enhancement. International Journal of Pure and Applied Mathematics 2010, 59(1):39-57.
14. Perelson A.S., Nelson P.W. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Review 1998, 41:3-44.
15. Pontryagin L., Boltyanskii V., Gamkrelidze R., Mishchenko E. The Mathematical Theory of Optimal Processes 1962, Wiley, New York.
16. Tan W.Y., Wu H. Stochastic modeling of the dynamics of CD4+ T-cell infection by HIV and some Monte Carlo studies. Mathematical Biosciences 1998, 147(2):173-205.
17. Von Stryk O., Bulirsch R. Direct and indirect methods for trajectory optimization. Annals of Operations Research 1992, 37(1):357-373.