Some state space models of HIV pathogenesis under treatment by anti- viral drugs in HIV-infected individuals

Mathematical Biosciences

Volumn 156, Issue 1-2, 1999, Pages 69-94

  Tan, Wai Yuan ^a   Xiang, Zhihua ^a  

^a University of Memphis   (United States)

Author keywords

Actively infected T cells; Extended Kalman filter; Infectious free HIV; Noninfectious free HIV; Protease inhibitor; Stochastic differential equations

Indexed keywords

ANTIVIRUS AGENT; PROTEINASE INHIBITOR;

ANTIVIRAL ACTIVITY; CONFERENCE PAPER; HUMAN IMMUNODEFICIENCY VIRUS INFECTION; MATHEMATICAL MODEL; PATHOGENESIS; STOCHASTIC MODEL; T LYMPHOCYTE ACTIVATION; VIRUS LOAD;

CD4 LYMPHOCYTE COUNT; CD4-POSITIVE T-LYMPHOCYTES; HIV; HIV INFECTIONS; HIV PROTEASE INHIBITORS; HUMANS; LINEAR MODELS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MONTE CARLO METHOD; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; RITONAVIR; RNA, VIRAL; STOCHASTIC PROCESSES; VIRAL LOAD;

HUMAN IMMUNODEFICIENCY VIRUS; RNA VIRUSES;

EID: 0032896058     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(98)10061-5     Document Type: Conference Paper

References (19)

1. Perelson A.S., Neumann A.U., Markowitz M., Leonard J.M., Ho D.D. HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science. 271:1996;1582.
2. + T-cell subpopulations. J. Theor. Biol. 170:1994;367.
3. D. Kirschner, A.S. Perelson, A model for the immune system response to HIV: AZT treatment studies, in: O. Arino, D.E. Axelrod, M. Kimmel (Eds.), Mathematical population Dynamics 3, Chapter 18, Wuerz Publishing, Winnipeg, Manitoba, Canada, 1993.
4. Fauci A.S. Immunopathogenic mechanisms in human immunodeficiency virus (HIV). Ann. Intern. Medicine. 114:1993;678.
5. + T cells. Math. Biosci. 114:1993;81.
6. Kirschner, D., Webb, G.F., A model for treatment strategy in the chemotherapy of AIDS, Bull. Math. Biology, 1997 (to appear).
7. Levy J.A. HIV research: a need to focus on the right target. Lancet. 345:1995;1619.
8. Ho D.D., Neumann A.U., Perelson A.S., Chen W., Leonard J.M., Markowitz M. Rapid turnover of plasma virus and CD4 lymphocytes in HIV-1 infection. Nature. 373:1995;123.
9. Wei X., Ghosh S.K., Taylor M.E., Johnson V.A., Emini E.A., Deutsch P., Lifson J.D., Bonhoeffer S., Nowak M.A., Hahn B.H., Saag M.S., Shaw G.M. Viral dynamics in human immunodeficiency virus type 1 infection. Nature. 373:1995;117.
10. D.D. Ho, Pathogenesis of HIV infection, New York Meeting, Aaron Diamond AIDS Research Center and New York University, New York, NY, 1996.
11. Ioannidis J.P.A., Cappelleri J.C., Lau J., Sacks H.S., Skolnik P.R. Predictive value of viral load measurements in asymptomatic untreated HIV-1 infection: A mathematical model. AIDS. 10:1996;225.
12. + T cell infection by HIV and some Monte Carlo studies. Math. Biosci. 147:1998;173.
13. A. Gelb, Applied Optimal Estimation, MIT, Cambridge, MA, 1974.
14. A.P. Sage, J.L. Melsa, Estimation Theory with Applications to Communications and Control, McGraw-Hill, New York, NY, 1971.
15. + T cell counts using nonlinear KALMAN filtering, paper presented at the 1996 Annual Statistical Meeting in Chicago, IL, August 4-8, 1996.
16. W.Y. Tan, Z. Xiang, A state space model of the HIV pathogenesis, in: M.A. Horn, G. Simnott and G. Webb (Ed.) Mathematical Models in Medicine and Health Sciences, Vanderbilt University Press, 1998 (in press).
17. D.E. Catlin, Estimation, Control and Discrete Kalman Filter, Springer, Berlin, 1989.
18. IMSL, MATH/LIBRARY User's Manual, IMSL, Houston, Berlin, TX, 1989.
19. W.Y. Tan, S. Yakowitz, Machine learning for Markov decision processes with application to an AIDS allocation problem, special issue of IEEE, 1997 (to appear).