Stochastic optimal therapy for enhanced immune response

Mathematical Biosciences

Volumn 191, Issue 2, 2004, Pages 123-142

  Stengel, Robert F ^a   Ghigliazza, Raffaele ^a  

^a Princeton University   (United States)

Author keywords

Drug therapy; Immune system; Stochastic optimal control

Indexed keywords

BIOINFORMATICS; HUMORAL IMMUNE RESPONSE; ORGAN HEALTH; STOCHASTIC OPTIMAL THERAPY;

ANTIBODIES; CELLS; FEEDBACK; MATHEMATICAL MODELS; MICROBIOLOGY; PATHOLOGY; PLASMAS; STOCHASTIC CONTROL SYSTEMS;

IMMUNOLOGY;

ANTIBODY; ANTIGEN;

IMMUNE RESPONSE;

ANALYTICAL ERROR; ANTIGEN BINDING; ARTICLE; COMPLEMENT ACTIVATION; FEEDBACK SYSTEM; HUMORAL IMMUNITY; INFECTION; MATHEMATICAL ANALYSIS; PATHOGENESIS; PHAGOCYTE; PLASMA CELL; STOCHASTIC MODEL;

ANTI-INFECTIVE AGENTS; ANTIBODY FORMATION; COMPUTER SIMULATION; FEEDBACK, BIOCHEMICAL; HUMANS; INFECTION; MODELS, IMMUNOLOGICAL; STOCHASTIC PROCESSES;

EID: 4444322393     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2004.06.004     Document Type: Article

References (44)

1. R.F. Stengel, R. Ghigliazza, N. Kulkarni, and O. Laplace Optimal control of innate immune response Optimal Contr. Appl. Methods 23 2002 91
2. R.F. Stengel, R. Ghigliazza, and N. Kulkarni Optimal enhancement of immune response Bioinformatics 18 2002 1227
3. C.A. Janeway, P. Travers, M. Walport, and M. Shlomchik Immunobiology 2001 Garland London
4. P.M. Lydyard, A. Whelan, and M.W. Fanger Instant Notes in Immunology 2000 Springer New York
5. M. Thain, and M. Hickman The Penguin Dictionary of Biology 2000 Penguin Books London
6. A. Asachenkov, G. Marchuk, R. Mohler, and S. Zuev Disease Dynamics 1994 Birkhauser Boston
7. A. Rundell, H. HogenEsch, R. DeCarlo, Enhanced modeling of the immune system to incorporate natural killer cells and memory, in: Proc. Amer. Control Conf., Seattle, 1995, p. 255
8. A.S. Perelson Immunology for physicists Rev. Modern Phys. 69 1997 1219
9. M.A. Nowak, and R.M. May Virus Dynamics: Mathematical Principles of Immunology and Virology 2000 Oxford University Oxford
10. M.A. Nowak, R.M. May, R.E. Phillips, S. Rowland-Jones, D.G. Lalloo, S. McAdam, P. Klenerman, B. Köppe, K. Sigmund, C.R.M. Bangham, and A.J. McMichael Antigenic oscillations and shifting immunodominance in HIV-1 infections Nature 375 1995 606
11. A.S. Perelson, A.V. Neumann, M. Markowitz, J.M. Leonard, and D.D. Ho HIV-1 dynamics in vivo: virion clearance rate, infected cell lifespan, and viral generation time Science 271 1995 1582
12. A.S. Perelson, and P.W. Nelson Mathematical analysis of HIV-1 dynamics in vivo SIAM Rev. 41 1999 3
13. D. Wodarz, R.M. May, and M.A. Nowak The role of antigen-independent persistence of memory cytotoxic T lymphocytes Int. Immun. 12 2000 467
14. M.A. Stafford, Y. Cao, D.D. Ho, L. Corey, and A.S. Perelson Modeling plasma virus concentration and CD4+ T cell kinetics during primary HIV infection J. Theor. Biol. 203 2000 285
15. D. Wodarz, and M.A. Nowak CD8 memory, immunodominance, and antigenic escape Eur. J. Immun. 30 2000 2704
16. N. Wiener Cybernetics: or Control and Communication in the Animal and the Machine 1948 Technology Cambridge
17. R.E. Bellman Mathematical Methods in Medicine 1983 World Scientific Press Singapore
18. G.W. Swan Optimal control applications in biomedical engineering - a survey Opt. Contr. Appl. Methods 2 1981 311
19. G.W. Swan Applications of Optimal Control Theory in Medicine 1984 Marcel Dekker New York
20. G.W. Swan Role of optimal control theory in cancer therapy Math. Biosci. 101 1990 237
21. A.S. Perelson Applications of optimal control theory to immunology R.R. Mohler A. Ruberti Recent Developments in Variable Structure Systems Economics and Biology 1978 Springer Berlin 272
22. A.S. Perelson, M. Mirmirani, and G.F. Oster Optimal strategies in immunology, I: B-cell differentiation and proliferation J. Math. Biol. 3 1976 325
23. A.S. Perelson, M. Mirmirani, and G.F. Oster Optimal strategies in immunology, II: B memory cell production J. Math. Biol. 5 1978 213
24. A.S. Perelson, B. Goldstein, and S. Rocklin Optimal strategies in immunology, III: the IgM-IgG switch J. Math. Biol. 10 1980 209
25. D. Kirschner, S. Lenhart, and S. Serbin Optimal control of the chemotherapy of HIV J. Math. Biol. 35 1997 775
26. L.M. Wein, S.A. Zenios, and M.A. Nowak Dynamic multidrug therapies for HIV: a control theoretic approach J. Theor. Biol. 185 1997 15
27. S. Bonhoeffer, R.M. May, G.M. Shaw, and M.A. Nowak Virus dynamics and drug therapy Proc. Natl. Acad. Sci. USA 94 1997 6971
28. L.M. Wein, R.M. D'Amato, and A.S. Perelson Mathematical analysis of antiretroviral therapy aimed at HIV-1 eradication or maintenance of low viral loads J. Theor. Biol. 192 1998 81
29. D. Wodarz, and M.A. Nowak Specific therapy regimes could lead to long-term immunological control of HIV Proc. Natl. Acad. Sci. USA 96 1999 14464
30. D. Wodarz, K.M. Page, R.A. Arnaout, A.R. Thomsen, J.D. Lifson, and M.A. Nowak A new theory of cytotoxic T-lymphocyte memory: implications for HIV treatment Philos. Trans. Roy. Soc. B 355 2000 329
31. J.M. van Rossum, O. Steyger, T. van Uem, G.J. Binkhorst, and R.A.A. Maes Pharmacokinetics by using mathematical systems dynamics J. Eisenfeld M. Witten Modelling of Biomedical Systems 1986 Elsevier Science Publishers 121
32. D.C. Robinson Principles of pharmacokinetics R. Maronde Topics in Clinical Pharmacology and Therapeutics 1986 Springer New York 1
33. D.J. Bell, and F. Katusiime A time-optimal drug displacement problem Optimal Contr. Appl. Methods 1 1980 217
34. E.R. Carson, D.G. Cramp, L. Finkelstein, and D. Ingram Control System Concepts and Approaches in Clinical Medicine, Computers and Control in Clinical Medicine 1985 Plenum New York p. 1
35. H.J. Chizeck, and P.G. Katona Closed-loop control E.R. Carson D.G. Cramp Computers and Control in Clinical Medicine 1985 Plenum Press New York 95
36. A. Schumitsky Stochastic control of pharmacokinetic systems R.F. Maronde Topics in Clinical Pharmacology and Therapeutics 1986 Springer New York 13
37. R.W. Jelliffe Clinical applications of pharmacokinetics and control theory: planning, monitoring, and adjusting regimens of aminoglycosides lidocaine digitoxin and digoxin R.F. Maronde Topics in Clinical Pharmacology and Therapeutics 1986 Springer New York 26
38. M.M. Polycarpou, J.Y. Conway, Modeling and control of drug delivery systems using adaptive neural control methods, in: Proc. Amer. Control Conf., Seattle, 1996, p. 781
39. G.K. Kwong, K.E. Kwok, B.A. Finegan, S.L. Shah, Clinical evaluation of long range adaptive control for mean arterial blood pressure regulation, in: Proc. Amer. Control Conf., Seattle, 1996, p. 786
40. A. Gentilini, M. Morari, C. Bieniok, R. Wymann, T. Schnider, Closed-loop control of analgesia in humans, in: Proc. IEEE Conf. Decision and Control, Orlando, 2001, p. 861
41. R.S. Parker, F.J. Doyle, III, J.E. Harting, N.A. Peppas, Model predictive control for infusion pump insulin delivery, in: Proc. 18th Ann. Conf. IEEE Engineering in Medicine and Biology Soc., Amsterdam, 1996, p. 1822
42. R.F. Stengel Optimal Control and Estimation 1994 Dover Publications New York
43. R.E. Kalman, and R.S. Bucy New results in linear filtering and prediction ASME Trans. J. Basic Eng. 82D 1961 95
44. T. Kailath Linear Systems 1980 Prentice-Hall Englewood Cliffs