This study presents a mathematical modeling approach to the planning of HIV therapies on an individual basis. The model replicates clinical data from typical-progressors to AIDS for all stages of the disease with good agreement. Clinical data from rapid-progressors and long-term non-progressors is also matched by estimation of immune system parameters only. The ability of the model to reproduce these phenomena validates the formulation, a fact which is exploited in the investigation of effective therapies. The therapy investigation suggests that, unlike continuous therapy, structured treatment interruptions (STIs) are able to control the increase in both the drug-sensitive and drug-resistant virus population and, hence, prevent the ultimate progression from HIV to AIDS. The optimization results further suggest that even patients characterised by the same progression type can respond very differently to the same treatment and that the latter should be designed on a case-by-case basis. Such a methodology is presented here.
[1] S. Khalili and A. Armaou, "An extracellular stochastic model of early
HIV infection and the formulation of optimal treatment policy", Chem.
Eng. Sci., vol. 63, pp. 4361-4372, 2008.
[2] B. M. Adams, H. T. Banks, and H. Kwon, "Dynamic multidrug therapies
for HIV: optimal and STI control approaches", Math. Biosci. Eng.,
vol. 1, pp. 223-241, 2004.
[3] O. Krakovska and L. M. Wahl, "Drug-sparing regimens for HIV combination
therapy: benefits predicted for drug coasting", Bull. Math.
Biol., vol. 69, pp. 2627-2647, 2007.
[4] L. Rong, M. A. Gilchrist, Z. Feng, "Modelling within-host HIV-1
dynamics and the evolution of drug resistance: trade-offs between viral
enzyme function and drug susceptibility", J. Theor. Biol., vol. 247,
pp. 804-818, 2007.
[5] S. H. Bajaria, G. Webb, M. Cloyd, "Dynamics of nave and memory
CD4+ T lymphocytes in HIV-1 disease progression", JAIDS, vol. 30,
pp. 41-58, 2002.
[6] S. H. Bajaria, G. Webb, and D. E. Kirschner, "Predicting differential
responses to structured treatment interruptions during HAART", Bull.
Math. Biol., vol. 66, pp. 1093-1118, 2004.
[7] T. W. Chun, R. Davey, and D. Engel, "Re-emergence of HIV after
stopping therapy", Nature, vol. 401, pp. 874-875, 1999.
[8] M. A. Nowak and A. J. McMichael, "How HIV defeats the immune
system", Scientific American, pp. 58-65, 1995.
[9] M. M. Hadjiandreou, R. Conejeros, and D. I. Wilson, "Long-term
HIV dynamics subject to continuous therapy and structured treatment
interruptions", Chem. Eng. Sci., vol. 64, pp. 1600-1617, 2009.
[10] M. A. Nowak, R. M. May, "Virus dynamics: Mathematical principles
of immunology and virology", New York: Oxford University Press,
2000.
[11] T. Igarashi, C. R. Brown, Y. Endo, "Macrophages are the principal
reservoir and sustain high virus loads in rhesus macaques following the
depletion following the depletion of CD4+ T-cells by a highly pathogenic
SHIV: implications for HIV-1 infections of man", PNAS, vol. 98, pp.
658-663, 2001.
[12] K. S. Dorman, A. H. Kaplan, K. Lange, "Mutation takes no vacation:
can structured treatment interruptions increase the risk of drug-resistant
HIV-1?", JAIDS, vol. 25, pp. 398-402, 2000.
[13] D. E. Kirschner and A. S. Perelson, "A model for the immune system
response to HIV: AZT treatment studies", In: O. Arino, D. Axelrod,
M. Kimmel, editors, Mathematical population dynamics: analysis of
heterogeneity and theory of epidemics, Winnipeg: Wuerz Publishing,
pp. 295, 1995.
[14] D. E. Kirschner and G. F. Webb, "A mathematical model of combined
drug therapy of HIV infection", J. Theor. Med., vol. 1, pp. 25-34,
1997.
[15] J. Velasco-Hemandez, J. A. Garcia, and D. E. Kirschner, "Remarks
on modeling host-viral dynamics and treatment", In: C. Chavez,
S. Blower, P. Van Den Dreische, editors. Mathematical Approaches
for Emerging and Reemerging Infectious Diseases: An Introduction to
Models, Methods and Theory, vols. 1 and 2, New York: Springer-Verlag,
2001.
[16] Wolfram Research, Inc., Mathematica, Version 5.1, Champaign, IL,
U.S, 2004.
[17] F. M. Campello de Souza, "Modeling the dynamics of HIV-1 and CD4
and CD8 lymphocytes", IEEE Eng. Med. Biol., vol. 18, pp. 21-24,
1999.
[18] A. S. Fauci, G. Pantaleo, S. Stanley, "Immunopathogenic mechanisms
of HIV infection", Annals of Internal Medicine, vol. 124, pp. 654-663,
1996.
[19] J. B. Margolick, A. D. Donnenberg, and A. Munoz, "T Lymphocytes
homeostasis after seroconversion", JAIDS, vol. 7, pp. 415-416, 1994.
[20] E. Pennisi, J. Cohen, "Eradicating HIV from a patient: not just a
dream?", Science, vol. 272, pp. 1884, 1996.
[21] E. Vergu, A. Mallet, and J. Golmard, "A modeling approach to the
impact of HIV mutations on the immune system", Comput. Biol.
Med., vol. 35, pp. 1-24, 2005.
[22] R. F. Stengel, "Mutation and control of the human immunodeficiency
virus", Math. Biosci., vol. 213, pp. 93-102, 2008.
[23] M. M. Hadjiandreou, R. Conejeros, and V. S. Vassiliadis, "Towards
a long-term model construction for the dynamic simulation of HIV
infection", Math. Biosci. Eng., vol. 4, pp. 489-504, 2007.
[24] R. A. Filter, X. Xia, and C. M. Gray, "Dynamic HIV/AIDS parameter
estimation with application to a vaccine readiness study in Southern
Africa", IEEE Trans. Biomed. Eng., vol. 52, pp. 784-791, 2005.
[25] C. A. Sabin, H. Devereux, A. N. Phillips, "Course of viral load
throughout HIV-1 infection", JAIDS, vol. 23, pp. 172-177, 2000.
[26] S. LeBlanc, "The long and the short of AIDS Progression", The Bay
Area Reporter, 1996.
[27] M. Comar, C. Simonelli, S. Zanussi, "Dynamics of HIV-1 mRNA
expression in patients with long-term nonprogressive HIV-1 infection",
J. Clin. Invest., vol. 100, pp. 893-900, 1997.
[28] T. E. Yamashita, J. P. Phair, A. Munoz, "Immunologic and virologic
response to highly active antiretroviral therapy in the Multicenter AIDS
Cohort Study", AIDS, vol. 15, pp. 735-746, 2001.
[29] R. B. Markham, W. Wang, A. E. Weisstein, "Patterns of HIV-1 evolution
in individuals with differing rates of CD4 T cell decline", PNAS, vol.
95, pp. 12568-12573, 1998.
[30] T. C. Greenough, D. B. Brettler, F. Kirchhoff, "Long-term nonprogressive
infection with human immunodeficiency virus type in a
hemophilia cohort", J. Infect. Dis., vol. 180, pp. 1790-1802, 1999.
[31] The Body Health Resources Corporation, Drug Side Effects Chart,
[Online] Available: http://www.thebody.com/pinf/sideeffectchart.html
(accessed in 2007).
[32] M. Joly and J. M. Pinto, "Role of mathematical modeling on the optimal
control of HIV-1 pathogenesis", AIChEJ, vol. 52, pp. 856-885, 2006.
[33] gPROMS Advanced User Guide, Release 2.3. 2004. Process System
Enterprise Ltd, United Kingdom.
[34] R. S. Braithwaite, A. C. Justice, C. C. Chang, "Estimating the proportion
of patients infected with HIV who will die of comorbid diseases", Am.
J. Med., vol. 118, pp. 890-898, 2005.
[35] C. T. Fang, H. M. Hsu, S. J. Twu, "Decreased HIV transmission after
policy of providing free access to highly active antiretroviral therapy in
Taiwan", J. Infect. Dis., vol. 190, pp. 879-885, 2004.
[36] A. D. Paltiel, M. C. Weinstein, A. D. Kimmel, "The qualitative nature
of the primary immune response to HIV infection is a prognosticator of
disease progression independent of the initial level of plasma viremia",
PNAS, vol. 94, pp. 254-258, 1997.
[37] "Antiretroviral Guidelines 2006". Department of Health
and Human Services, pp. 1-113. [Online] Available:
http://www.aidsinfo.nih.gov/ContentFiles/ AdultandAdolescentsGL.pdf.
Accessed (March 2007).
[38] J. Lawrence, D. L. Mayers, K. H. Hullsiek, "Structured treatment interruption
in patients with multidrug-resistant human immunodeficiency
virus", N. Engl. J. Med., vol. 349, pp. 837-846, 2003.
[39] L. Ruiz, E. Ribera, A. Bonjoch, "Role of structured treatment interruption
before a 5-drug salvage antiretroviral regimen: the retrogene study",
J. Infect. Dis., vol. 188, pp. 977-985, 2003.
[40] T. Hraba, J. Dolezal, "A mathematical model and CD4+ lymphocyte
dynamics in HIV infection", Em. Infect. Dis., pp. 299-305, 1996.
[41] UK Group on Transmitted HIV Drug Resistance, "Time trends in
primary resistance to HIV drugs in the United Kingdom: multicentre
observational study", BMJ, vol. 331, pp. 1368-1371, 2005.
[42] Y. Huang, S. L. Rosenkranz, H. Wu, "Modeling HIV dynamics and
antiviral response with consideration of time-varying drug exposures,
adherence, and phenotypic sensitiviry", Math. Biosci., vol. 184, pp.
165- 186, 2003.
[43] V. Novk, I. Perfilieva, and J. Mockor, Mathematical principles of fuzzy
logic, USA: Kluwer Academic Publishers, 1999.
[44] GlaxoSmithKline, Product Information. 2005. [Online] Available:
http://www.gsk.com/products/prescriptionmedicines.shtml.
[45] Abbott Laboratories, Product Information. 2006. [Online] Available:
http://www.norvir.com/hiv/hiv0044.htm.
[46] F. T. Aweeka, M. Kang, J-Y Yu, "Pharmacokinetic evaluation of the
effects of ribavirin on zidovudine triphosphate formation: ACTG 5092s
Study Team", HIV Medicine, vol. 8, pp. 288-294, 2007.
[47] B. S. Kappelhoff, A. D. R. Huitema, K. M. L. Crommentuyn, "Development
and validation of a population pharmacokinetic model for ritonavir
used as a booster or as an antiviral agent in HIV-1-infected patients",
Br. J. Clin. Pharmacol., vol. 59, pp. 174-182, 2004.
[48] M. Legrand, E. Comets, G. Aymard, "An in vivo pharmacokinetic/
pharmacodynamic model for antiretroviral combination", HIV
Clin. Trials, vol. 4, pp. 170/183, 2003.
[1] S. Khalili and A. Armaou, "An extracellular stochastic model of early
HIV infection and the formulation of optimal treatment policy", Chem.
Eng. Sci., vol. 63, pp. 4361-4372, 2008.
[2] B. M. Adams, H. T. Banks, and H. Kwon, "Dynamic multidrug therapies
for HIV: optimal and STI control approaches", Math. Biosci. Eng.,
vol. 1, pp. 223-241, 2004.
[3] O. Krakovska and L. M. Wahl, "Drug-sparing regimens for HIV combination
therapy: benefits predicted for drug coasting", Bull. Math.
Biol., vol. 69, pp. 2627-2647, 2007.
[4] L. Rong, M. A. Gilchrist, Z. Feng, "Modelling within-host HIV-1
dynamics and the evolution of drug resistance: trade-offs between viral
enzyme function and drug susceptibility", J. Theor. Biol., vol. 247,
pp. 804-818, 2007.
[5] S. H. Bajaria, G. Webb, M. Cloyd, "Dynamics of nave and memory
CD4+ T lymphocytes in HIV-1 disease progression", JAIDS, vol. 30,
pp. 41-58, 2002.
[6] S. H. Bajaria, G. Webb, and D. E. Kirschner, "Predicting differential
responses to structured treatment interruptions during HAART", Bull.
Math. Biol., vol. 66, pp. 1093-1118, 2004.
[7] T. W. Chun, R. Davey, and D. Engel, "Re-emergence of HIV after
stopping therapy", Nature, vol. 401, pp. 874-875, 1999.
[8] M. A. Nowak and A. J. McMichael, "How HIV defeats the immune
system", Scientific American, pp. 58-65, 1995.
[9] M. M. Hadjiandreou, R. Conejeros, and D. I. Wilson, "Long-term
HIV dynamics subject to continuous therapy and structured treatment
interruptions", Chem. Eng. Sci., vol. 64, pp. 1600-1617, 2009.
[10] M. A. Nowak, R. M. May, "Virus dynamics: Mathematical principles
of immunology and virology", New York: Oxford University Press,
2000.
[11] T. Igarashi, C. R. Brown, Y. Endo, "Macrophages are the principal
reservoir and sustain high virus loads in rhesus macaques following the
depletion following the depletion of CD4+ T-cells by a highly pathogenic
SHIV: implications for HIV-1 infections of man", PNAS, vol. 98, pp.
658-663, 2001.
[12] K. S. Dorman, A. H. Kaplan, K. Lange, "Mutation takes no vacation:
can structured treatment interruptions increase the risk of drug-resistant
HIV-1?", JAIDS, vol. 25, pp. 398-402, 2000.
[13] D. E. Kirschner and A. S. Perelson, "A model for the immune system
response to HIV: AZT treatment studies", In: O. Arino, D. Axelrod,
M. Kimmel, editors, Mathematical population dynamics: analysis of
heterogeneity and theory of epidemics, Winnipeg: Wuerz Publishing,
pp. 295, 1995.
[14] D. E. Kirschner and G. F. Webb, "A mathematical model of combined
drug therapy of HIV infection", J. Theor. Med., vol. 1, pp. 25-34,
1997.
[15] J. Velasco-Hemandez, J. A. Garcia, and D. E. Kirschner, "Remarks
on modeling host-viral dynamics and treatment", In: C. Chavez,
S. Blower, P. Van Den Dreische, editors. Mathematical Approaches
for Emerging and Reemerging Infectious Diseases: An Introduction to
Models, Methods and Theory, vols. 1 and 2, New York: Springer-Verlag,
2001.
[16] Wolfram Research, Inc., Mathematica, Version 5.1, Champaign, IL,
U.S, 2004.
[17] F. M. Campello de Souza, "Modeling the dynamics of HIV-1 and CD4
and CD8 lymphocytes", IEEE Eng. Med. Biol., vol. 18, pp. 21-24,
1999.
[18] A. S. Fauci, G. Pantaleo, S. Stanley, "Immunopathogenic mechanisms
of HIV infection", Annals of Internal Medicine, vol. 124, pp. 654-663,
1996.
[19] J. B. Margolick, A. D. Donnenberg, and A. Munoz, "T Lymphocytes
homeostasis after seroconversion", JAIDS, vol. 7, pp. 415-416, 1994.
[20] E. Pennisi, J. Cohen, "Eradicating HIV from a patient: not just a
dream?", Science, vol. 272, pp. 1884, 1996.
[21] E. Vergu, A. Mallet, and J. Golmard, "A modeling approach to the
impact of HIV mutations on the immune system", Comput. Biol.
Med., vol. 35, pp. 1-24, 2005.
[22] R. F. Stengel, "Mutation and control of the human immunodeficiency
virus", Math. Biosci., vol. 213, pp. 93-102, 2008.
[23] M. M. Hadjiandreou, R. Conejeros, and V. S. Vassiliadis, "Towards
a long-term model construction for the dynamic simulation of HIV
infection", Math. Biosci. Eng., vol. 4, pp. 489-504, 2007.
[24] R. A. Filter, X. Xia, and C. M. Gray, "Dynamic HIV/AIDS parameter
estimation with application to a vaccine readiness study in Southern
Africa", IEEE Trans. Biomed. Eng., vol. 52, pp. 784-791, 2005.
[25] C. A. Sabin, H. Devereux, A. N. Phillips, "Course of viral load
throughout HIV-1 infection", JAIDS, vol. 23, pp. 172-177, 2000.
[26] S. LeBlanc, "The long and the short of AIDS Progression", The Bay
Area Reporter, 1996.
[27] M. Comar, C. Simonelli, S. Zanussi, "Dynamics of HIV-1 mRNA
expression in patients with long-term nonprogressive HIV-1 infection",
J. Clin. Invest., vol. 100, pp. 893-900, 1997.
[28] T. E. Yamashita, J. P. Phair, A. Munoz, "Immunologic and virologic
response to highly active antiretroviral therapy in the Multicenter AIDS
Cohort Study", AIDS, vol. 15, pp. 735-746, 2001.
[29] R. B. Markham, W. Wang, A. E. Weisstein, "Patterns of HIV-1 evolution
in individuals with differing rates of CD4 T cell decline", PNAS, vol.
95, pp. 12568-12573, 1998.
[30] T. C. Greenough, D. B. Brettler, F. Kirchhoff, "Long-term nonprogressive
infection with human immunodeficiency virus type in a
hemophilia cohort", J. Infect. Dis., vol. 180, pp. 1790-1802, 1999.
[31] The Body Health Resources Corporation, Drug Side Effects Chart,
[Online] Available: http://www.thebody.com/pinf/sideeffectchart.html
(accessed in 2007).
[32] M. Joly and J. M. Pinto, "Role of mathematical modeling on the optimal
control of HIV-1 pathogenesis", AIChEJ, vol. 52, pp. 856-885, 2006.
[33] gPROMS Advanced User Guide, Release 2.3. 2004. Process System
Enterprise Ltd, United Kingdom.
[34] R. S. Braithwaite, A. C. Justice, C. C. Chang, "Estimating the proportion
of patients infected with HIV who will die of comorbid diseases", Am.
J. Med., vol. 118, pp. 890-898, 2005.
[35] C. T. Fang, H. M. Hsu, S. J. Twu, "Decreased HIV transmission after
policy of providing free access to highly active antiretroviral therapy in
Taiwan", J. Infect. Dis., vol. 190, pp. 879-885, 2004.
[36] A. D. Paltiel, M. C. Weinstein, A. D. Kimmel, "The qualitative nature
of the primary immune response to HIV infection is a prognosticator of
disease progression independent of the initial level of plasma viremia",
PNAS, vol. 94, pp. 254-258, 1997.
[37] "Antiretroviral Guidelines 2006". Department of Health
and Human Services, pp. 1-113. [Online] Available:
http://www.aidsinfo.nih.gov/ContentFiles/ AdultandAdolescentsGL.pdf.
Accessed (March 2007).
[38] J. Lawrence, D. L. Mayers, K. H. Hullsiek, "Structured treatment interruption
in patients with multidrug-resistant human immunodeficiency
virus", N. Engl. J. Med., vol. 349, pp. 837-846, 2003.
[39] L. Ruiz, E. Ribera, A. Bonjoch, "Role of structured treatment interruption
before a 5-drug salvage antiretroviral regimen: the retrogene study",
J. Infect. Dis., vol. 188, pp. 977-985, 2003.
[40] T. Hraba, J. Dolezal, "A mathematical model and CD4+ lymphocyte
dynamics in HIV infection", Em. Infect. Dis., pp. 299-305, 1996.
[41] UK Group on Transmitted HIV Drug Resistance, "Time trends in
primary resistance to HIV drugs in the United Kingdom: multicentre
observational study", BMJ, vol. 331, pp. 1368-1371, 2005.
[42] Y. Huang, S. L. Rosenkranz, H. Wu, "Modeling HIV dynamics and
antiviral response with consideration of time-varying drug exposures,
adherence, and phenotypic sensitiviry", Math. Biosci., vol. 184, pp.
165- 186, 2003.
[43] V. Novk, I. Perfilieva, and J. Mockor, Mathematical principles of fuzzy
logic, USA: Kluwer Academic Publishers, 1999.
[44] GlaxoSmithKline, Product Information. 2005. [Online] Available:
http://www.gsk.com/products/prescriptionmedicines.shtml.
[45] Abbott Laboratories, Product Information. 2006. [Online] Available:
http://www.norvir.com/hiv/hiv0044.htm.
[46] F. T. Aweeka, M. Kang, J-Y Yu, "Pharmacokinetic evaluation of the
effects of ribavirin on zidovudine triphosphate formation: ACTG 5092s
Study Team", HIV Medicine, vol. 8, pp. 288-294, 2007.
[47] B. S. Kappelhoff, A. D. R. Huitema, K. M. L. Crommentuyn, "Development
and validation of a population pharmacokinetic model for ritonavir
used as a booster or as an antiviral agent in HIV-1-infected patients",
Br. J. Clin. Pharmacol., vol. 59, pp. 174-182, 2004.
[48] M. Legrand, E. Comets, G. Aymard, "An in vivo pharmacokinetic/
pharmacodynamic model for antiretroviral combination", HIV
Clin. Trials, vol. 4, pp. 170/183, 2003.
@article{"International Journal of Biological, Life and Agricultural Sciences:57604", author = "Marios M. Hadjiandreou and Raul Conejeros and Ian Wilson", title = "HIV Treatment Planning on a case-by-CASE Basis", abstract = "This study presents a mathematical modeling approach to the planning of HIV therapies on an individual basis. The model replicates clinical data from typical-progressors to AIDS for all stages of the disease with good agreement. Clinical data from rapid-progressors and long-term non-progressors is also matched by estimation of immune system parameters only. The ability of the model to reproduce these phenomena validates the formulation, a fact which is exploited in the investigation of effective therapies. The therapy investigation suggests that, unlike continuous therapy, structured treatment interruptions (STIs) are able to control the increase in both the drug-sensitive and drug-resistant virus population and, hence, prevent the ultimate progression from HIV to AIDS. The optimization results further suggest that even patients characterised by the same progression type can respond very differently to the same treatment and that the latter should be designed on a case-by-case basis. Such a methodology is presented here.
", keywords = "AIDS, chemotherapy, mathematical modeling, optimal control, progression.", volume = "3", number = "8", pages = "394-10", }
