Incorporation of variability into the modeling of viral delays in HIV infection dynamics

Mathematical Biosciences

Volumn 183, Issue 1, 2003, Pages 63-91

  Banks, H T ^a   Bortz, D M ^b   Holte, S E ^c  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c Fred Hutchinson Cancer Research Center   (United States)

Author keywords

Eclipse phase; HIV pathogenesis; Non linear delay equations; Variability

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; VIRUSES;

TEMPORAL DELAYS;

PATHOLOGY;

HUMAN IMMUNODEFICIENCY VIRUS;

ANALYSIS OF VARIANCE; ARTICLE; DATA ANALYSIS; FINITE ELEMENT ANALYSIS; HUMAN IMMUNODEFICIENCY VIRUS INFECTION; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; METHODOLOGY; NONHUMAN; NONLINEAR SYSTEM; PARAMETER; PATHOGENESIS; PROBABILITY; SIMULATION; THEORETICAL STUDY; VIRULENCE;

EID: 0037401144     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(02)00218-3     Document Type: Article

References (68)

1. E. Pisani, B. Schwartländer, S. Cherney, A. Winter (Eds.), Global Summary of the HIV/AIDS Epidemic, end 1999, Joint United Nations Programme on HIV/AIDS, 2000.
2. P.W. Nelson, J.E. Mittler, A.S. Perelson, Effect of drug efficacy and the eclipse phase of the viral life cycle on estimates of HIV viral dynamic parameters, J. AIDS 26 (2001) 405.
3. M. Emerman, personal communication, Nov. 2000.
4. J.E. Mittler, B. Sulzer, A.U. Neumann, A.S. Perelson, Influence of delayed viral production on viral dynamics in HIV-1 infected patients, Math. Biosci. 152 (1998) 143.
5. S. Holte, M. Emerman, A competition model for viral inhibition of host cell proliferation, Math. Biosci. 166 (2000) 69.
6. D.D. Ho, A.U. Neumann, A.S. Perelson, W. Chen, J.M. Leonard, M. Markowitz, Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection, Nature 373 (1995) 123.
7. A.S. Perelson, A.U. Neumann, M. Markowitz, J.M. Leonard, D.D. Ho, HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Science 271 (1996) 1582.
8. X. Wei, S.K. Ghosh, M.E. Taylor, V.A. Johnson, E.A. Emini, P. Deutsch, J.D. Lifson, S. Bonhoeffer, M.A. Nowak, B.H. Hahn, M.S. Saag, G.M. Shaw, Viral dynamics in human immunodeficiency virus type 1 infection, Nature 373 (1995) 117.
9. J.E. Mittler, M. Markowitz, D.D. Ho, A.S. Perelson, Improved estimates for HIV-1 clearance rate and intracellular delay, AIDS 13 (1999) 1415.
10. A.S. Perelson, P. Essunger, Y. Cao, M. Vesanen, A. Hurley, K. Saksela, M. Markowitz, D.D. Ho, Decay characteristics of HIV-1-infected compartments during combination therapy, Nature 387 (1997) 188.
11. B. Ramratnam, S. Bonhoeffer, J. Binley, A. Hurley, L. Zhang, J.E. Mittler, M. Markowitz, J.P. Moore, A.S. Perelson, D.D. Ho, Rapid production and clearance of HIV-1 and hepatitis C virus assessed by large volume plasma apheresis, The Lancet 354 (1999) 1782.
12. D.S. Callaway, A.S. Perelson, HIV-1 infection and low steady state viral loads, Bull. Math. Biol. 64 (2002) 29.
13. I. Kramer, Modeling the dynamical impact of HIV on the immune system: Viral clearance, infection, and AIDS, Math. Comput. Modell. 29 (1999) 95.
14. H.A. Monteiro, C.H.O. Gongalves, J.R.C. Piqueira, A condition for successful escape of a mutant after primary HIV infection, J. Theoret. Biol. 203 (2000) 399.
15. J.M. Murray, G. Kaufmann, A.D. Kelleher, D.A. Cooper, A model of primary HIV-1 infection, Math. Biosci. 154 (1998) 57.
16. M.A. Nowak, S. Bonhoeffer, G.M. Shaw, R.M. May, Anti-viral drug treatment: Dynamics of resistance in free virus and infected cell populations, J. Theor. Biol. 184 (1997) 203.
17. A.N. Phillips, Reduction of HIV concentration during acute infection: Independence from a specific immune response, Science 271 (1996) 497.
18. M.A. Stafford, L. Corey, Y. Cao, E.S. Daar, D.D. Ho, A.S. Perelson, Modeling plasma virus concentration during primary HIV infection, J. Theor. Biol. 203 (2000) 285.
19. L.M. Wein, R.M. D'Amato, 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.
20. D. Wodarz, V.A.A. Jansen, The role of T cell help for anti-viral CTL responses, J. Theor. Biol. 211 (2001) 419.
21. D. Wodarz, A.L. Lloyd, V.A.A. Jansen, M.A. Nowak, Dynamics of macrophage and t cell infection by HIV, J. Theor. Biol. 196 (1999) 101.
22. Z. Grossman, M. Feinberg, V. Kuznetsov, D. Dimitrov, W. Paul, HIV infection: how effective is drug combination treatment? Immunol. Today 19 (1998) 528.
23. Z. Grossman, M. Polis, M.B. Feinberg, I. Levi, S. Jankelevich, R. Yarchoan, J. Boon, F. de Wolf, J.M.A. Lange, J. Goudsmit, D.S. Dimitrov, W.E. Paul, Ongoing HIV dissemination during HAART, Nature Med. 5 (1999) 1099.
24. A.V.M. Herz, S. Bonhoeffer, R.M. Anderson, R.M. May, M.A. Nowak, Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay, Proc. Nat. Acad. Sci. USA 93 (1996) 7247-7251.
25. A.L. Lloyd, The dependence of viral parameter estimates on the assumed viral load life cycle: limitations of studies of viral load data, Proc. Roy. Soc. Lond. B 268 (2001) 847.
26. P.W. Nelson, J.D. Murray, A.S. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Math. Biosci. 163 (2000) 201.
27. P.W. Nelson, A.S. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Biosci. 179 (2002) 73.
28. R.V. Culshaw, S. Ruan, A delay-differential equation model of HIV infection of CD4+ T-cells, Math. Biosci. 165 (2000) 27.
29. J. Tam, Delay effect in a model for virus replication, IMA J. Math. Appl. Med. Biol. 16 (1999) 29.
30. A. Kamina, R.W. Makuch, H. Zhao, Stochastic modeling of early HIV-1 population dynamics, Math. Biosci. 170 (2001) 187.
31. W. Tan, H. Wu, Stochastic modeling of the dynamics of CD4+ T-cell infection by HIV and some Monte Carlo studies, Math. Biosci. 147 (1998) 173.
32. W. Tan, Z. Xiang, Some state space models of HIV pathogenesis under treatment by anti-viral drugs in HIV-infected individuals, Math. Biosci. 156 (69) (1999) 69.
33. H.C. Tuckwell, E.L. Corfec, A stochastic model for early HIV-1 population dynamics, J. Theor. Biol. 195 (1998) 451.
34. D. Wick, S.G. Self, Early HIV infection in vivo: Branching-process model for studying timing of immune responses and drug therapy, Math. Biosci. 165 (2000) 115.
35. H. Wu, A.A. Ding, V. de Gruttola, Estimation of HIV dynamic parameters, Stat. Medicine 17 (1998) 2463.
36. D. Kirschner, S. Lenhart, S. Serbin, Optimal control of chemotherapy of HIV, J. Math. Biol. 35 (1997) 775.
37. L.M. Wein, S.A. Zeinos, M.A. Nowak, Dynamic multidrug therapies for HIV: A control theoretic approach, J. Theor. Biol. 185 (1997) 15.
38. A.B. Gumel, P.N. Shivakumar, B.M. Sahai, A mathematical model for the dynamics of HIV-1 during the typical course of infection, Nonlinear Analy. 47 (2001) 1773.
39. D. Verotta, F. Schaedeli, Non-linear dynamics models characterizing long-term virological data from AIDS clinical trials, Math. Biosci. 176 (2002) 163.
40. M.A. Nowak, R.M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University, New York, NY, 2000.
41. A.S. Perelson, Modeling viral and immune system dynamics, Nature Rev. Immunol. 2 (2002) 28.
42. A.S. Perelson, P.W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev. 41 (1999) 3.
43. D.R. Cox, H.D. Miller, The Theory of Stochastic Processes, Chapman and Hall, London, 1965.
44. A. Jensen, An elucidation of Erlang's statistical works through the theory of stochastic processes, in: E. Brockmeyer, H.L. Halstrom, A. Jensen (Eds.), The Life and Works of A.K. Erlang, The Copenhagen Telephone Company, Copenhagen, 1948, p. 23.
45. A.L. Llyod, Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods, Proc. Roy. Soc. Lond. B 268 (2001) 985.
46. N. MacDonald, Biological Delay Systems: Linear Stability Theory, Cambridge University, Cambridge, 1989.
47. H.T. Banks, Identification of nonlinear delay systems using spline methods, in: V. Lakshmikantham (Ed.), Nonlinear Phenomena in Mathematical Sciences, Academic Press, New York, NY, 1982, p. 47.
48. H.T. Banks, J.A. Burns, Hereditary control problems: Numerical methods based on averaging approximations, SIAM J. Control Optim. 16 (1978) 169.
49. H.T. Banks, F. Kappel, Spline approximations for functional differential equations, J. Diff. Eqs. 34 (1979) 496.
50. F. Frisch, H. Holme, The characteristic solution of a mixed difference and differential equation occurring in economic dynamics, Econometrica 3 (1935) 225.
51. G.E. Hutchinson, Circular causal systems in ecology, Ann. New York Acad. Sci. 50 (1948) 221.
52. N. Minorsky, Self-excited oscillations in a dynamical system possessing retarded actions, J. Appl. Mech. 9 (1942) 65.
53. R.M. May, Stability and Complexity in Model Ecosystems, Princeton University, Princeton, NJ, 2001 (orignially published 1973).
54. J.D. Murray, Mathematical Biology, Biomathematics, vol. 19, Springer, New York, NY, 1989.
55. R. Bellman, K.L. Cooke, Differential-Difference Equations, Mathematics in Science and Engineering, vol. 6, Academic Press, New York, NY, 1963.
56. R.D. Driver, Ordinary and Delay Differential Equations, Applied Mathematical Sciences, vol. 20, Springer, New York, NY, 1977.
57. J.M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics, vol. 20, Springer, New York, NY, 1977.
58. Y. Kuang, Delay Differential Equations With Applications in Population Dynamics, no. 191 in Mathematics in Science and Engineering, Academic Press, New York, NY, 1993.
59. O. Diekmann, S.A. van Gils, S.M.V. Lunel, H.O. Walther, Delay Equations: Functional-, Complex-, and Nonlinear Analysis, Applied Mathematical Sciences, vol. 110, Springer, New York, NY, 1995.
60. H. Górecki, S. Fuksa, P. Grabowski, A. Korytowski, Analysis and Synthesis of Time Delay Systems, John Wiley, New York, NY, 1989.
61. J.K. Hale, S.M.V. Lunel, Introduction to Functional Differential Equations, Applied Mathematical Sciences, vol. 99, Springer, New York, NY, 1993.
62. D.M. Bortz, R. Guy, J. Hood, K. Kirkpatrick, V. Nguyen, V. Shimanovich, Modeling HIV infection dynamics using delay equations, Tech. Rep. CRSC-TR00-24, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, in: P.A. Gremaud, Z. Li, R.C. Smith, H.T. Tran (Eds.), Proceedings of the 2000 Industrial Mathematics Modeling Workshop for Graduate Students, Oct. 2000.
63. M.E. Rogel, L.I. Wu, M. Emerman, The human immunodeficiency virus type 1 vpr gene prevents cell proliferation during chronic infection, J. Virol. 69 (1995) 882.
64. F.C. Hoppensteadt, Mathematical Methods of Population Biology, Cambridge University, Cambridge, 1982.
65. D.M. Bortz, Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations, Ph.D. dissertation, North Carolina State University, Raleigh, NC, 2002.
66. H.T. Banks, B.G. Fitzpatrick, Statistical methods for model comparison in parameter estimation problems for distributed systems, J. Math. Biol. 28 (1990) 501.
67. H.T. Banks, D.M. Bortz, A parameter sensitivity methodology in the context of HIV delay equation models, Tech. Rep. CRSC-TR02-24, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, Aug. 2002; J. Math. Biol., submitted for publication.
68. H.T. Banks, K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhäuser, Boston, MA, 1989.